# 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.

336 questions
Filter by
Sorted by
Tagged with
45 views

### Universality and continuous variation of critical exponent close to a tricritical point

A tricritical point is a point at which a second order transition line and a first order transition line merge. At equilibrium, this point can be described by a landau potential (see for example this ...
• 1,168
190 views

• 33
38 views

### Meaning of $n$-critical point

My lecture notes about field theory refer to a tricritical point as a point in which a continuous phase transition line meets a discontinuous phase transition line. In the following it refers to a ...
69 views

### Calculating higher-order correlation functions of the Ising model

I'm trying to compute the correlation functions $<s_1...s_n>$ of specific n-spin subsets as a function of the temperature in systems with up to $N=256^2$ spins. These will be used to compute ...
1 vote
65 views

### Why are Critical Exponents simple non-integer powers?

I'm reading Baxter's Exactly Solved Models in Statistical Physics, and he claims that for $$t=\frac{T-T_c}{T_c}$$ which is just a change of variable in temperature to centre and normalise w.r.t. the ...
• 383
59 views

• 3,098
1 vote
74 views

### What is a name of a critical point?

Imagine a critical line separating two thermodynamic phases. There is a point on this line splitting the line into two pieces such that on one piece the transition between the two phases is 1st order, ...
• 11
1 vote
60 views

### New Universality Classes and Multiple Transition Points in Systems [closed]

I'm currently exploring several concepts related to universality classes, phase transitions, and critical phenomena. My questions revolve around the comprehensiveness of universality classes, the ...
• 167
39 views

### Ferromagnetic Potts models in a field and the endpoint of their first-order lines

The $q=3$, $d=3$ ferromagnetic Potts model has a first-order transition on varying temperature. I recently learned that at small $h>0$, where $h$ is a field favoring one of the three colors, there ...
• 2,292
75 views

### Does there exist a 2d continuous phase transition that is first-order in mean-field theory and satisfies the Harris criterion $\nu>1$?

I am looking for an example of a clean, local $d=2$ classical model that undergoes a continuous phase transition on varying temperature that satisfies two properties: The phase transition is ...
• 2,292
257 views
+250

### How much does quantum uncertainty contribute to the uncertainty of earthquakes?

More abstractly, the topic is: amplification of quantum uncertainty within dynamically unstable systems. I'd like to have a calculable toy model, e.g. maybe a quantum version of the famous "...
• 13.1k
1 vote
120 views

### Why are domain sizes of all lengths when the correlation length is infinite at $T_c$?

Given that the correlation length diverges at the critical point, why are domains of finite size? What is the relationship for a ferromagnet between correlation length and domain size?
• 31
90 views

45 views

### Equivalent definitions of (dis)continuous phase transitions at criticality

Consider a classical lattice model on $\mathbb{Z}^d$ and suppose that the system undergoes a phase transition as you lower the temperature, i.e., increase $\beta$. The most general definition of a ...
• 2,123
71 views

### Two-dimensional Ising model for square lattices

Consider Onsager's exact solution of two-dimensional Ising model for square lattices with nearest neighbour interaction energy ‘J ‘being equal in the horizontal and vertical directions. At the ...
1k views

### Why is the correlation length finite for a first order phase transition?

In Statistical mechanics textbooks it is usually purported that first order phase transitions have a finite correlation length $\xi$. Why is that and/or how can we derive that?
• 183
17 views

### Connectivity of random geometric graph with open boundary conditions

I have a question regarding the existence of a closed-form solution of the connectivity in terms of the radius of vertices (disks) in a two-dimensional ($d=2$) random geometric graph (RGG) with open ...
1 vote
118 views

### Mean field calculation of the Critical dynamic exponent $z$

In the prediction of the Kibble-Zurek-Mechanism for defects correlation length and relaxation time which are for 2D melting described by the KTHNY (Kosterlitz-Thouless-Halperin-Nelson-Young theory, ...
256 views

### Binder cumulant method for non-Gaussian distributions

In the Ising model, we know that the order parameter $m$ has a Gaussian distribution for temperatures below the critical point. Measuring the exact point where this phase transition takes place was ...
73 views

### 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 ...
• 81
448 views

### 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 ...
• 904
1 vote
67 views

### 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 ...
• 3,256
61 views

119 views

• 248
222 views

### 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 ...
• 2,292
72 views

### 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 ...
• 49.9k
1 vote
74 views

### 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 ...
• 22.1k
255 views

### 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 ...
• 823
65 views

### 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 $$Z=\int D\theta(x)\,exp(-\frac{K}{2\pi}\int d^{2}x\,(\nabla_x\theta)^2),$$...
• 868
45 views

### 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 ...
• 1,904
116 views

### 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 ...
• 60.3k