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Questions tagged [critical-phenomena]

The physics of critical phenomena is the physics of systems close to a critical point, like the critical temperature in a ferromagnetic transition or the critical point of a gas-liquid transition. Examples of critical phenomena include dynamical slowing down, divergence of correlation length and ergodicity breaking.

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71
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3answers
60k views

First and second order phase transitions

Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article starts by explaining that Ehrenfest's original definition was that a first-order ...
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2k views

Examples of important known universality classes besides Ising

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
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455 views

Fluids with critical point at ordinary temperature and pressure

Are there any fluids with critical point near STP or that are supercritical at STP? If not would it be feasible to design a molecule for a substance with critical point near STP using theoretical/...
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0answers
448 views

Measure of Lee-Yang zeros

Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
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780 views

Are the first order phase transitions always associated with a latent heat?

Is the first order ferromagnetic transition below the critical temperature associated with latent heat? For example, the transition of ferromagnetic configuration with all its spins aligned up to a ...
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1answer
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Why are there large fluctuations at the critical point and why does Landau theory work despite such large fluctuations?

The question is about the critical point in a second-order phase transition: Why do fluctuations become so large at the critical point? As I understand, Landau’s theory of phase transition is some ...
10
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1answer
254 views

Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
10
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1answer
478 views

Conversion of results between cutoff regularization and dimensional regularization

Generally it would be expected that a renormalizable/physical quantum field theory (QFT) would be regularization independent. For this I would first fix my regularization scheme and then compute stuff....
9
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1answer
596 views

Why are the eigenvalues of a linearized RG transformation real?

The RG transformation $R_\ell$ maps a set of coupling constants $[K]$ of a model Hamiltonian to a new set of coupling constants $[K']=R_\ell[K]$ of a coarse-grained model where the length scale is ...
8
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704 views

Why is the correlation function a power law at the critical point?

I’m taking my first exam in statistical field theory and critical phenomena. I’ve reached a point in which we use the fact that the pair correlation function decays as a power law at the critical ...
8
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1answer
146 views

Can thermodynamics be relied at the critical point?

Thermodynamics neglects fluctuations and deals with average macroscopic quantities (which is also important for the extensity of extensive thermodynamics coordinates e.g., the internal energy ${\rm U}$...
8
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1answer
149 views

What is energy in $z \neq 1 $ theories?

In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
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304 views

What's about the critical exponents and RG flow in upper critical dimension $D=4$?

We know when $D>4$, i.e. $D$ larger than upper critical dimension, then critical exponents are exactly same as the ones of mean field . When $D<4$, critical exponents are not given correctly by ...
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327 views

Is there a spin glass version of Prince Rupert's Drop?

Spin Glasses are known to converge to their ground state under Simulated Annealing. The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
6
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3answers
257 views

Non-uniqueness of the Order Parameter and its Critical Exponent

In the theory of phase transitions, an order parameter is usually defined as some quantity which distinguishes the two phases of the system by being zero in one phase, and non-zero in the other (see e....
6
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1answer
263 views

How close to the critical point is sufficient close for measuring critical exponents?

I am learning Monte Carlo and just manage to simulate a phase transition by computing the heat capacity or the susceptibility. I wish I can also compute critical exponents.To this purpose, I have read ...
6
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1answer
388 views

Beyond the Ginzburg-Landau-Wilson theory/renormalization group

In the famous seminal paper by K G Wilson and J Kogut in Physics Reports (Aug 1974) on The renormalization group and the ε expansion, they achieve a pinnacle of uniting the Ginzburg-Landau theory and ...
6
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1answer
148 views

Pink noise in low-dimensional systems

Pink noise (1/f) is often cited as a signature of complex or critical systems. Is it possible for a low-dimensional time-independent first-order system to generate pink noise? Intuitively it seems ...
5
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3answers
870 views

Free energy functions are analytic or non-analytic in phase transitions?

I already saw this Phys.SE post and it seems perfectly reasonable that the free energy describing a system must be a non-analytic function in order to display a phase transition. An analytic ...
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2answers
796 views

Why is a critical system equal to a gapless system?

In condensed matter physics, people often say that a system without energy gap is a critical system. What does it mean? Any help is appreciated!
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1answer
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Critical temperature and lattice size with the Wolff algorithm for 2d Ising model

When I run my implementation of the Wolff algorithm on the square Ising model at the theoretical critical temperature I get subcritical behaviour. The lattice primarily just oscillates between mostly ...
5
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1answer
4k views

How to measure the spin-spin correlation in a Monte Carlo simulation of the Ising model?

I'm simulating the Ising Model in 2D up to 5D and I want to calculate the spin-spin correlation, correlation length, and critical exponent of the system. What is a good way to go about doing this? ...
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2answers
227 views

Nontrivial critical exponents in exactly solvable models?

Are there any exactly solvable models in statistical mechanics that are known to have critical exponents different from those in mean-field theory, apart from the two-dimensional Ising model? I wonder ...
5
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1answer
97 views

Integrability of a non-integrable quantum spin model at critical point

Is it right, that non-integrable quantum spin models in one dimension become integrable at their critical points? Or do they stay nonintegrable at the critical point also? Are there any examples known?...
5
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1answer
94 views

How does the transition to turbulence happen in incompressible fluids?

The question is difficult to understand unless I explain why I am asking it. I would not really be interested in Fluid Dynamics if the transition to turbulent flow were not, at least approximately, ...
5
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2answers
213 views

Is the Landau free energy scale-invariant at the critical point?

My question is different but based on the same quote from Wikipedia as here. According to Wikipedia, In statistical mechanics, scale invariance is a feature of phase transitions. The key ...
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69 views

What are the excitations in the near critical 2D-Ising model in a magnetic field?

Apparently it is well known that the 2D Ising model with $T=T_C$ in a small magnetic field has a mass gap and correlation length $\xi \sim h^{- \frac{8}{15}} $. Further, in a paper in 1989 ...
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1answer
87 views

What is the topology of a phase diagram?

Looking at various two-variable phase diagrams I was struck by that on every one I have seen so far all the phases formed simple connected regions; see, for example the phase diagrams of $H_2O$ or of $...
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510 views

Failure of Hertz-Millis-Moriya theory for quantum phenomena

In the quantum critical phenomena of condensed matter, the earlier work by Hertz, Moriya and Millis develope the the Hertz-Millis-Moriya (HMM) theory of quantum phase transition. Naively, they ...
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197 views

Nature of phase transitions in Kitaev honeycomb model

Short version of my question is this : what is the nature of the phase transition in the Kitaev honeycomb model ? Longer version: Kitaev honeycomb model undergoes a phase transition from a gapped to ...
4
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1answer
434 views

Scale invariance at phase transitions

The Wikipedia entry for scale invariance states In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical ...
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2answers
178 views

Divergent Coulomb integrals in superfluid fluctuations

In Chapter 3 of Kardar's statistical physics of fields, in the context of lower critical dimension, he works out an example about superfluids where starting from the probablity of a particular ...
4
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1answer
3k views

Why do spin correlation functions in Ising Models decay exponentially below the critical temperature?

I'm trying to form a better understanding of the 2D Ising Model, in particular the behaviour of the correlation functions between spins of distance $r$. I've found a number of explanatory texts that ...
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2answers
2k views

Why correlation length diverges at critical point?

I want to ask about the behavior near critical point. Let me take an example of ferromagnet. At $T < T_c$, all spins are aligned to the same direction thus it is in the ordered state, scale ...
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3answers
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Does wax go through a sharp phase transition when it melts?

When ice melts, the system goes sharply from being solid to being liquid. There is no intermediate state where it is soft. This is a true phase transition. The thermodynamic potential is not an ...
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2answers
725 views

The relation between critical surface and the (renormalization) fixed point

In the book, I read some remarks about the criticality: Iterations of the renormalization (group) map generate a sequence of points in the space of couplings, which we call a renormalization group ...
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1answer
143 views

Is there any model in statistical physics which has the ratio of specific heat exponent to correlation length exponent, $\alpha/\nu \approx 2.44$?

I am simulating a disordered ising-like model in 2d whose phase transition is expected to be continuous, whose universality class is as yet unknown. By plotting the Specific heat scaling function, i.e....
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1answer
462 views

Second derivative of vapor pressure from a cubic equation of state

It is quite easy to compute the first derivative of vapor pressure with respect to temperature from a cubic equation of state at least at the critical point since there is a continuity with the ...
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2answers
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1D Ising Model with different boundary conditions

The Hamiltonian for one-dimensional Ising model is given by, \begin{equation} \mathcal{H} = -J\sum_{<ij>} S_iS_j; \quad i,j=1,2,...,N+1 \end{equation} where $<ij>$ denotes that there is ...
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0answers
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Renormalization Group - Scaling fields and physical critical exponents (1D Ising model)

This is related to this question: Critical exponents and scaling dimensions from RG theory. TLDR: How to compute physical critical exponents $\alpha, \beta, \gamma, etc$ from the RG exponents when ...
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80 views

How does renormalization relate to emergence?

In statistical mechanics renormalization is often related to coarse-graining which in turn allows to calculate some macroscopic states. The resulting macroscopic description is sometimes called ...
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363 views

Critical temperature difference between Ising and XY model

The following formula gives the critical coupling (more precisely the ratio of the spin-spin coupling over the temperature) for $O(n)$ models on a triangular lattice: $$\text{e}^{-2K}=\frac{1}{\sqrt{...
3
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1answer
271 views

What is the meaning of “Deconfined Quantum Critical Point”?

I tried to google it but couldn't found an intuitive explanation (not existing in Wikipedia). I have also tried to read the Science paper by T. Senthil et al, but couldn't fully understand the ...
3
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3answers
330 views

What does “no characteristic length or time scale” mean?

When looking into the topic of "self-organized criticality," (SOC) one often comes across descriptions of SOC as a state where "the system has no characteristic length or time scale." (Examples here ...
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2answers
252 views

Why does a vanishing energy gap indicate a phase transition?

More concretely: When looking at the Ising model in the description of Bogoliubov fermions, we get an explicit expression for the energy gap, that vanishes for a particular value of the magnetic field....
3
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3answers
440 views

Landau and Mean Field Theory

I have often heard that the Landau theory of phase transitions is a mean field theory. Why is this so? What is the connection between the two ideas? One stresses symmetry breaking and one averages the ...
3
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1answer
52 views

why do matrix product states work at critical point?

Matrix product states satisfy the entanglement area law, which should be a property of gapped states. But usually, MPS work well in 1D quantum phase transition problems. As far as I know, ...
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1answer
104 views

Why is it interesting to study “quantum quench” at a critical point?

In the presentation, "Quantum Quenches in Extended Systems", by S. Sotiriadis, P. Calabrese and J. Cardy, it was pointed out that quatum quench through a critical point remains an open problem. Why ...
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1answer
212 views

What's the critical temperature of the XY model on a triangular lattice

I've been looking deeply into many bibliographic references without finding the answer. I would be interested in knowing the numerical value of the critical 2d XY spin model on triangular lattice. ...
3
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2answers
266 views

Self-organized criticality and the butterfly effect

We know that in a critical system and for self-organized criticality we have long range interactions due to power-law decay of correlation. Is this fact equivalent to the butterfly effect?