# 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.

145 questions
Filter by
Sorted by
Tagged with
16 views

### Flow velocity ambiguity in transition region

I have calculated the following short table concerning the stationary flow of water in a 1 meter long pipe with a diameter of 16 mm and a completely smooth inner surface. The flow is driven by the ...
153 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 ...
140 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 ...
41 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, ...
20 views

### How to get mean field critical exponents for this Hamiltonian?

$$\mathcal{H} = -J \sum_{\langle ij\rangle} \sum_{\alpha=1}^N s_i{}^\alpha s_j{}^\alpha -g \sum_{\langle ij\rangle} \sum_{\alpha\beta} (s_i{}^\alpha s_j{}^\alpha) (s_i{}^\beta s_j{}^\beta)$$ Above ...
41 views

### Derivation of the Ising free energy close to a critical point

In "Statistical physics of fields" Mehran Kardar states that the Ising free energy scales with, $$f(t,h)\sim t^\alpha g_f\left(\frac{h}{t^\Delta}\right),$$ wherein $t=\vert T-T_c\vert/T_c$ ...
194 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 ...
16 views

### What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)?

What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)? For instance, the classical XY model has KTc/J = 0.898 and the quantum XY model with S=1/2 ...
44 views

### Ferromagnet $\leftrightarrow$ paramagnet at Curie temperature

I think it's like this: $\, m=\tanh\left(\frac{Bμ}{k_bT}\right)$. If now the temperature decreases, then $\mu$ increases, until it flattens out ($\tanh$ function). Is the a point where $m$ flats out, ...
51 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 ...
173 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 ...
42 views

### How to deduce the formula of the Correlation Length on a periodic lattice?

Sometimes in Monte Carlo simulations we need to compute the correlation length, but this is a hard task without a formula. However, for instance, in an periodic cubic lattice of $L^3$ spins, some ...
74 views

### 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 ...
49 views

### Correlation function at zero distance

I'm confused about the definition of the correlation function (at equal time). I know it is defined from the thermal average of the scalar product of two random variables (for example the spins of a ...
9 views

### What’s the topology of critical region?

Duhem said the aim of physics is natural classification. I think topology and geometry are a wonderful way to link analogous parts among different phenomena. Thus we can classify and predict facts. ...
27 views

### Landau free energy expansion

On Huang page 417 he talks about Landau Theory and he says that in the neighborhood of a critical point where m(x) is small, we can expand the landau free energy $$\psi=\psi(m(x),H(x))$$ In powers ...
76 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?...
249 views

### Why is the upper critical dimension of the Ising model 4?

I have read in various sources, that the critical exponents of the Ising Model are identical to the meanfield ones for dimensions $d \geq 4$. In trying to understand this better I came across the ...
46 views

### What determines the specific value of the order parameter in spontaneous symmetry breaking?

Three examples in the spontaneous symmetry breaking that occurs at a phase transitions: A ferromagnet below the Curie temperature chooses an axis of quantisation along which all the spins align, ...
98 views

### Does the critical dynamical exponent z of a 2D Ising model (simulated with Metropolis) vary with the temperature?

I have found in the literature that the critical dynamical exponent $z$ of an Ising model simulated with a local algorithm (such as Metropolis) is something around 2 near the critical temperature, ...
57k 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 ...
71 views

### What is the meaning of $\lim_{x\to0}\frac{\ln|-x|}{\ln|x|}$? [closed]

I am now working out some critical exponent, and I encountered this result $$\lim_{x\to0}\frac{\ln|-x|}{\ln|x|}.$$ Can I write this equals to 1? Here $x=\frac{T-T_{c}}{T_{c}}$ and $T_{c}$ is the ...
65 views

### Why the correlation function of 2D classical XY model is written so?

2D classical XY model $$H = -J\cos(\theta_{i}-\theta_{j})%$$ is famous for Berezinskii-Kosterlitz-Thouless phase transition. This is because of the difference of correlation function between hot and ...
115 views

### Assumptions behind Ornstein-Zernike correlation function

Let $S(\mathbf q)$ be come correlation function in Fourier space ($\mathbf q$ = wavevector). In the study of condensed matter systems, I have often encountered the statements that a reasonable form ...
33 views

105 views

### Ising Model with site-dependent magnetic field

Consider an Ising system in an external field, which is different at different sites. The Hamiltonian of the system is given by $H = -J\sum_{<i,j>}^{}s_i s_j - \sum_{i}^{} h_i s_i$ Here each ...
104 views

### Why does Critical Points have fluctuations on all scales (Infinite correlation length?

I have been studying statistical field theory for a while and I still haven't found a physical explanation for this question. Every answer seems to be kind of circular. Basically something like this: "...
111 views

### Long Range order in 2D Ising model

We know from the exact solutions for 2D Ising model on square lattice the long range order appears bellow critical temperature, but how does this agree with the Mermin-Wagner theorem, from which we ...
304 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 ...
75 views

### Reaching critical point in a fluid

I have carbon dioxide in a pressure reactor. I can control both temperature and pressure inside the container (or, equivalently, temperature and amount of fluid). I need to reach the critical point in ...