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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Did Democritus predict atoms using Sharp Phase Transitions? How? Couldn't a classical field theory also have Sharp Phase Transitions?
In the Wikipedia page for the Ising Model it is written without citations:
One of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in ...
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Is the self-dual point always a critical point?
I was studying duality maps in my Advanced Stat. Mech. class and it was told that all self-dual points need not correspond to critical point. I understand that critical points are points where ...
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How was the critical exponents related to the scaling dimensions of the local operators?
On "The Conformal Bootstrap: Theory, Numerical Techniques, and Applications"(arXiv:1805.04405
) by David Poland, Slava Rychkov, Alessandro Vichi page 5
Consider for example the critical ...
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Combinatorics in $\lambda \phi^4$ theory and critical exponents
I am trying to understand critical phenomena from the perspective of Statistical Mechanics.
The interacting term in the $\lambda \phi^4$ scalar theory is usually (but not always) multiplied by $\frac{...
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Reference for critical exponents in a non standard derivation
I'm currently preparing an individual project about Landau theory of phase transitions. I think I understand well enough the standard procedure:
expand the free energy as $F(P, T, \phi) = F_0(P, T) + ...
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Why is a critical point defined as a stationary inflection point?
In the analysis of a van der Waals equation of state, it's quite clear that the temperature and pressure at which
$$
\left( \frac{\partial p}{\partial V} \right)_T = 0\\
\left( \frac{\partial^2 p}{\...
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Ising model phase transition when external magnetic field is non-zero
In the Ising model, when the external magnetic field is absent, it has a second order phase transition, because there is a discontinuity in the magnetic susceptibility vs Temperature, T (and magnetic ...
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Is it physically possible to bring water to its critical point?
I've been thinking about the critical point of water, which has three distinct and specific properties: critical temperature, critical pressure, and specific critical volume. However, when I draw a PV ...
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Transfer matrix for the calculation of average spin in ising model
Background
Consider 1-D Ising model of n lattice points with periodic boundary condition,
$\beta H(\sigma_1,\sigma_2,...,\sigma_N) = -\sum_{i=1}^nk(\sigma_i\sigma_{i+1})-\sum_{i=1}^n\sigma_i$
$k=\beta ...
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What is the physical meaning of critical points in black hole thermodynamic topics?
In black hole thermodynamic topics, the critical points sometimes calculate. They are introduced in different types and calculated in conventional forms.
Recently, in thermodynamic calculations, these ...
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Is renormalization different to just ignoring infinite expressions?
Looking into textbooks, I got the impression in renormalization perturbation theory one adds
counterterms to the Lagrangian to cancel terms (usually integrals) that are infinite.
My question is, could ...
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Is the lattice spacing $a$ a dangerously irrelevant parameter?
Near a renormalization group fixed point, we can perform a scale transformation of length $L' = b^{-1} L$. In this case the relative lattice spacing should transform as $a' = b^{-1} a$. After $n$ ...
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Deriving spatial correlation of the intensity of multifractal eigenstates
I am struggling how to derive the spatial correlation of the intensity of multifractal eigenstates. From the book '50 Years of Anderson Localization, page 114', the following correlation holds (Eq.(2....
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universality classes at critical point
It is known that the universality class of a given physical system undergoing a continuous phase transition depends only on the dimensionality and symmetries of the given system. My question is if ...
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Correlation function in the critical two-dimensional Ising model
Fifty years ago, McCoy and Wu in their book The Two-Dimensional Ising Model formulated a hypothesis about the correlation function in the critical two-dimensional Ising model. According to this ...
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Why is the supercritical fluid region a perfect rectangle?
The melting, sublimation and evaporation curves are all non straight lines in a (p,T) phase diagram, while the curves that divide liquid/gas regions from supercritical fluid region are perfectly ...
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Analyzing a Kawasaki-evolving Ising model? (conserved-order-parameter Ising model)
Focusing on 2D in further text
I am struggling to understand how the conserved-order-parameter Ising model (also known/reached through Kawasaki algorithm) shows criticality and also how it can be ...
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Extra term in $2+\epsilon$ expansion of sigma model
I'm working through David Tong's notes on Statistical Field Theory, in particular the $2+\epsilon$ expansion of the sigma model with free energy
$$F[\vec{n}]=\int d^dx \frac{1}{2e^2}\nabla\vec{n}\cdot\...
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Di Francesco et al.'s CFT - additional corrections to free-energy for strip geometries on a lattice?
In classical spin systems, there's a nice way to extract the central charge of the model by looking at finite-size corrections to the free energy of strips of length $L$ and width $W$ in the limit of ...
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Why is critical opalescence localized in this classroom demonstration?
In Baierlein's Thermal Physics, he describes a classroom demonstration:
A sealed vertical chamber contains a carefully measured amount of carbon dioxide under high pressure. To begin with, the system ...
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How does one get the uncertainties for the critical exponents in Metropolis Monte Carlo for the Ising model?
I've recently learned the basics about simulating the Ising model with Metropolis Monte Carlo. In particular, I've seen how to evolve the system, compute the average magnetization, find the critical ...
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How renormalization allows to describe critical point behaviour using the critical fixed point?
As in the title, I am trying to understand how the critical fixed point (CFP) can be used to derive the thermodynamic singular behavior of the physical critical point (PCP). The context I have in mind ...
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How to derive the long range behavior of XY model?
In a lecture note (Lec 23) by Sachdev (https://canvas.harvard.edu/courses/76589/files/folder/Lectures?), he considers a model
$$Z=\int D\theta(x)\,exp(-\frac{K}{2\pi}\int d^{2}x\,(\nabla_x\theta)^2),$$...
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Order Parameter for Gas-Liquid systems, analogy to magnetic case
I've read that the order parameter for gas-liquid systems is $m=\rho_l-\rho_g$, while the corresponding ordering field is $h=P-P_c$.
I have some issue with this, because it doesn't seem analogous to ...
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Was Big Bang a phase transition? [closed]
Was Big Bang a phase transition (critical phenomenon)? If "yes", what is the order parameter and what determined the value of the order parameter chosen?
When talking about phase transitions ...
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Order Parameter, Phase transition
Is order parameter for a phase transition is unique?
Is it always true that in one phase order parameter have zero value and in another phase it has non zero value?
Is there any standard rules for ...
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Goldstone Bosons and Criticality
In the presence of spontaneous symmetry breaking of a continuous symmetry, there are massless goldstone bosons. However, they are not treated in the discussions of critical phenomena. Naively I would ...
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Connection between the $\beta$-function and critical exponents
In my recent readings in QFT, I came across the fact that there is a connection between critical exponents in thermodynamics and the $\beta$-function of the renormalization group flow. Does anybody ...
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Zeros of multiplicative wave function renormalization
It is probably needless to recall here that the Reimann zeta function $$\zeta(s)=\sum_{n=1}^\infty n^{-s}$$ and its generalizations are among the central objects of study in mathematics.
The main open ...
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Dynamical critical exponent in stochastic vector model
For stochastic $O(N)$ model given by:
$$S[\psi,\phi]=\int \frac{d\omega\, dk^D}{(2\pi)^{D+1}} \left( \vec{\psi}(-k,-\omega).\vec{\phi}(k,\omega) \left(-i\omega + \gamma k^2+r \right) -2T\vec{\psi}(-k,-...
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Central limit theorem and fluctuations
Considering a statistical model away from its criticality, the system can be essentially viewed as a collection of subsystems of size $\xi^d$ (with $\xi$ the correlation length) with no mutual ...
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Who found the Ising transition?
The famous story is that Ernst Ising studied the 1d classical stat mech model which bears his name, argued it has no phase transition, and guessed that the same would hold in all dimensions. He was ...
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To what extent can phase transitions be made rigorous?
It seems a lot of physical intuition in statistical mechanics, for example phase transitions, critical temperature, scaling hypothesis, renormalization group methods etc. should have a purely ...
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Second partial derivatives of thermodynamics potentials at the critical point
I'm trying to understand the physics of phase transitions, specially at the critical point, but I find myself stuck.
For an hydrostatic system, I studied the stability conditions, that lead to (in the ...
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Why is the energy of a vortex in a superconductor finite?
I just had a glimpse of the Ginzburg-Landau theory of superconductivity. I am surprised that that the energy of a vortex is finite. This is surprising because as far as I know, in superfluids, the ...
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Critical exponents and scaling dimension
It is often stated that the scaling exponents, e.g. $\alpha$ and $\beta$, of the critical 2D Ising model are related to the scaling dimensions $\Delta_{\sigma}$ and $\Delta_{\epsilon}$ of the ...
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Could 2D critical quantum system be described by 3D conformal field theory?
It is well known that 1D quantum critial systems are described by 2D cft. Could 2D critical quantum system be described by 3D conformal field theory?
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Divergent or not? the heat capacity at the lambda point
In Kerson Huang's book (2nd edition, page 309), it is stated that at the lambda point, the heat capacity diverges logarithmically. But, in wiki, it is stated that it is finite.
https://en.wikipedia....
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How many universality classes are there in the universe?
There are more-than-we-can-count number of phases in the universe, all described by their interesting symmetries. But what about universality classes? Is the number just as big? Ising, Heisenberg, XY ...
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Is central charge related to symmetry?
I am currently reading the paper "Theory of finite-entanglement scaling at one-dimensional quantum critical points" by Pollmann et. al. and I am trying to understand the central charge in ...
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Question about the so-called upper critical dimension
It is often said that above the upper critical dimension, the mean field theory is correct. What is the precise meaning of this statement? Let us be specific and consider the $d$-dimensional Ising ...
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Is the transition from laminar flow to turbulent flow a kind of phase transition like those in condensed matter?
From the laminar flow to turbulent flow, is it a kind of phase transition?
If so, what is the critical point? And what about the correlation length behaviours and fluctuation? Any critical exponents?
...
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Lower bound on the spectral gap in finite size critical systems with locality
Local quantum systems tuned to criticality are gapless in the thermodynamic limit. The rate at which the ground state spectral gap approaches zero as the system size $L \rightarrow \infty$ carries ...
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If boiling of water involves change in internal energy, then why does the temperature remain constant?
According to the first law of thermodynamics,
$$\Delta Q=\Delta W+\Delta U$$
Considering boiling of water to be an isothermal process, $\Delta U$ should be zero, but then my textbook says: "we ...
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How to understand the notion of critical temperature in thermodynamics?
I just want to verify my understanding of the notion of critical temperature of fluids, because the more I read about it in the literature I become more and more confused.
My main clue for ...
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"Quantum" hyperscaling relation from a Renormalization Group (RG) viewpoint
Through the RG method, one can obtain the hyperscaling relation between the critical exponents of classical second-order phase transitions:
\begin{equation}
2-\alpha=\nu d
\end{equation}
In the case ...
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What is the difference between charge density wave (CDW) and charge ordering (CO)?
I am suffering with the terminology of condensed matter physics.
When I read papers about strongly correlated electron system, sometimes I see the words "charge density wave" (CDW) and "...
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Power-Spectrum for Self-Organised Criticality
In 1987 Bak, Tang and Weisenfeld authored a paper (link) on Self-Organised Criticality, on how minimally stable self-organised systems propagate the perturbations it is subjected to, scale-freely - ...
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What is the order of the transition for a 2D Ising model?
I have been running around the block trying to find answers for this question, and I keep running into caveats. So, I just want to write down the list of things I want to know:
Given that the order ...
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First-order phase transition in the Ising model?
I am doing a simulation of the 2D Ising model with a Monte Carlo algorithm. I think that the model should exhibit a second order phase transition at $\beta=\beta_c$, but when I try to plot the ...
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