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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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### 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 ...
415 views

### Is my interpretation of the fixed points of the renormalization group correct?

I would like to know whether or not I understood the meaning of the fixed points of the RG concerning the phase diagram of a system. This is how I understand it: Since a RG transformation leaves the ...
1k views

### What leads to the existence of critical temperature?

We know that $T_c$ is the temperature above which no amount of pressure could force a gas to liquefy. But why is this? Somehow I don't buy the point that the gas molecules exert too much pressure back ...
30k views

### What is the definition of correlation length for the Ising model?

The correlation length $\xi$ is related to critical temperature $T_c$ as $$\xi\sim|T-T_{c}|{}^{-\nu},$$ where $\nu$ is the critical exponent. Is this the formal definition of correlation length? ...
2k 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 ...
5k 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 ...
6k 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? ...
2k 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 ...
1k 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 ...
453 views

### What are conditions for the existence of a critical value (for a phase transition)?

Can there only be a critical temperature if there is some natural unit for an observable in the model, i.e. if there is a natural scale for something? Otherwise I don't see how for a system there ...
1k views

### Van der Waals model for liquid gas phase transition : Understanding Maxwell construction

I have a question on the context of Maxwell construction, spinodal lines. In this pdf https://www.uam.es/personal_pdi/ciencias/evelasco/master/tema_III.pdf they first compute the Van der Waals model ...
2k views

### What is the physical meaning of "correlation length"?

I am studying phase transitions right now and trying to understand the physical meaning of the concept correlation length. I saw the equations but I still couldn't quite wrap my head around the ...
3k 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 ...
1k views

### 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 ...
700 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....
2k 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 ...
4k 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 ...
2k views

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### Is combustion a phase transition?

Is combustion a phase transition? Premise If we take a chemical reaction $$A + B \leftrightarrow AB,$$ we expect all the three chemicals, $A,B, AB$ to be present in the mixture, in the proportions ...
10k 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? ...
1 vote
479 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 ...
1 vote
896 views

### Is there any zero-order phase transition in nature?

Theoretically, a finite jump in the free energy phase diagrams can naturally be called a zeroth-order phase transition according to the Ehrenfest classification. We always hear about the first- and ...
162 views

### Examples of phase transition nuclei whose dynamics impede their own growth?

I recently asked a question over on the Earth Science stack exchange about cumulus cloud formation from (roughly) point sources. These points can form around the same time across large areas, such as ...
If $\hat{m_z}=\frac{1}{N}\sum_i \hat{\sigma^z_i}$ is an order parameter for finite quantum system (transverse Ising model, say), then it will never break the $\mathbb{Z}_2$ symmetry since \$\langle\...