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1answer
73 views

Understanding this metaphor involving e-mails, chaos and phase transitions [closed]

I asked this question on the English Stack Exchange and people advised to try get the answer here. I can’t get the idea of metaphor in the last sentence of the following quote: Instead, email ...
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0answers
39 views

Nature of phase transitions in quantum mechanical systems

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 ...
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0answers
53 views

Can the terms in the microscopic model with nonzero conformal spin generate some new term(s) under RG (renormalization group) flow?

As in the book Bosonization and Strongly Correlated Systems at page 66, it says that "We see that the original perturbation with nonzero conformal spin generates the perturbation with zero conformal ...
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1answer
40 views

AdS/CFT and Kondo problem/ Ginzburg-Landau theory

I was reading the review on Unconventional superconductivity by Mike Norman, towards the end (page 22) he comments two things about AdS/CMT: "In the condensed matter context in two dimensions, one ...
4
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1answer
99 views

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 ...
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1answer
69 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 ...
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0answers
80 views

How are the real-space RG transformations defined?

I'm reading Shang-keng Ma's book Modern theory of critical phenomena, and I'm a bit confused as to how the real-space RG transformations are defined. Ma basically says that these transformations are ...
1
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1answer
66 views

Criticality in BCS Theory

Can someone provide me with a pedagogical introduction into the role of criticality in BCS theory? The QCD condensate is due to strong coupling. The BCS condensation involves only weak coupling - ...
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0answers
54 views

Why does correlation length diverge at the critical point?

In thermodynamics, the correlation length diverges near the critical point on the phase diagram, I'd like to understand why this is the case. I've found a few different papers / books, but most only ...
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0answers
13 views

How to visualize that the critical flow conditions in a heat added flow remains constant?

In a variable area nozzle, where compressibility is observable, if the flow goes from point A to point B and heat addition is considered. How do we see that the critical speed of sound (imaginary ...
0
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1answer
29 views

Criticality and the number of paths on a lattice

In the review "Scaling, universality, and renormalization: Three pillars of modern critical phenomena" by Stanley, he makes the following claim towards the end of the paper, which is neither derived ...
3
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1answer
117 views

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 ...
4
votes
3answers
249 views

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 ...
0
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1answer
48 views

What is the length dimension in critical phenomena?

In this question it is said that: The best way to numerically work with continuous phase transitions is to study observables that have a vanishing length dimension (or mass dimension in the ...
0
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0answers
37 views

How to interpret a null critical exponent?

In the 2D Ising model the value for $\alpha$ is $0$, but I fail to see how we can have this if the specific heat of the system actually has a divergence in the critical temperature. I've seen this ...
0
votes
4answers
129 views

What is the state of water at exactly 0°C?

Theoretically speaking, what is the state of water at bang on 0°C - not any lower or higher? Any lower would make it a solid whereas any higher would make it a liquid. But what about bang on 0°C? ...
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2answers
140 views

Good layman definition of the critical point(phases) and supercriticality

I've heard of this point among others, but never really got what it meant. Wikipedia makes one's head spin. The only thing I picked up is that it occurs between liquid and gas, and displays ...
0
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1answer
63 views

Is the Landau Free Energy U-TS or βH?

I'm having a hard time figuring out the physical meaning of the Landau Free Energy density: $$f(\phi,\nabla\phi,T) = \frac{1}{2}|\nabla\phi |^2 + \frac{a(T-T_c)}{2}|\phi |^2 + \frac{b}{4}|\phi |^4$$ ...
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1answer
410 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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0answers
95 views

Ising model Monte Carlo simulations in 4D and 5D

I'm going to be simulating the Ising Model in 4D and above to calculate spin-spin correlations and critical exponents and am wondering how to tackle this algorithmically. For example, in 1D, use an ...
1
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0answers
69 views

Books/resources for statistical field theory

I was wondering if anyone knows good, approachable textbook or other resources about statistical field theory (topics like in Kardar's Statistical physics of fields: lattice models, mean field theory, ...
3
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0answers
66 views

Example of critical (non-relativistic) quantum field theory in 1D?

Is there an example of a critical non-relativistic bosonic quantum field theory in 1D (no time)? So, the field theory can be describe by annihilation, $\psi(x)$, and creation operators, ...
5
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0answers
133 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 ...
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0answers
51 views

What is the central charge of the disordered $q$-state Potts model, for large $q$?

The central charge of a model, is, heuristically related to the number of microscopic degrees of freedom. Is there a simple argument for the asymptotic behavior of the central charge for the ...
3
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0answers
35 views

References or resource recommendation for the mathematics concerning fission

I am working on a statistical problem that appears similar (in some respects...) to nuclear fission. I am interested in the properties of a system undergoing fission around, or near, delayed ...
5
votes
1answer
150 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 ...
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0answers
644 views

List of known universality classes

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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0answers
147 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 ...
7
votes
1answer
225 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 ...
5
votes
1answer
112 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, ...
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1answer
53 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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0answers
146 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: ...
3
votes
2answers
99 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 ...
3
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0answers
80 views

Neel order and O(3) model

The coarse grained fluctuations of the Neel order parameter in the half integer spin anti-ferromagnetic Heisenberg model is described by the O(3) non-linear sigma model with a strange berry phase ...
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3answers
1k views

Formula for critical mass? Critical mass of polonium?

I'm looking for the critical mass of Polonium; is there a formula? E.g.:$$\text{Neutrons / Protons}\cdot\text{ Constant = X kg}$$ There is a little table in the Wikipedia. E.g.: ...
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2answers
231 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. ...
3
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0answers
225 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 ...
1
vote
1answer
218 views

Is water a gas at critical density, room temperature?

I am quoting Chaikin, Lubensky, Principles of Condensed Matter Physics, p. 4. Now suppose we have a closed container of water vapor at a density of 0.322 g/cc at room temperature. As the ...
1
vote
1answer
216 views

Infinite-range 1D Ising model

The Hamiltonian for this system is given by \begin{equation} \mathcal{H} \{S\} = -H\sum_i S_i - \frac{J_0}{2} \sum_{ij} S_i S_j, \end{equation} where $H$ is the external magnetic field and there is no ...
3
votes
2answers
786 views

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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1answer
122 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 ...
1
vote
1answer
645 views

Andrew's experiment

In Thomas Andrew's experiment, consider the dome shaped saturation region. If we increase the pressure at constant volume until we reach the critical point, why does the density of vapours rise and ...
4
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2answers
408 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!
9
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0answers
181 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 ...