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.

67 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
14
votes
0answers
452 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 ...
5
votes
0answers
70 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 ...
5
votes
1answer
90 views

What is the topology of a phase diagram?

Looking at various two-variable phase diagrams I was struck by that on every one I have seen so far all the phases formed simple connected regions; see, for example the phase diagrams of $H_2O$ or of $...
5
votes
0answers
519 views

Failure of Hertz-Millis-Moriya theory for quantum phenomena

In the quantum critical phenomena of condensed matter, the earlier work by Hertz, Moriya and Millis develope the the Hertz-Millis-Moriya (HMM) theory of quantum phase transition. Naively, they ...
5
votes
0answers
200 views

Nature of phase transitions in Kitaev honeycomb model

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 ...
4
votes
0answers
92 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 ...
4
votes
0answers
80 views

How does renormalization relate to emergence?

In statistical mechanics renormalization is often related to coarse-graining which in turn allows to calculate some macroscopic states. The resulting macroscopic description is sometimes called ...
4
votes
0answers
370 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: $$\text{e}^{-2K}=\frac{1}{\sqrt{...
3
votes
0answers
60 views

Relation between scaling dimension and critical exponents for harmonic peturbations in $O(N)$ Wilson-Fisher (WF) in an old paper

I am reading the paper "Harmonic perturbations of generalized Heisenberg spin systems" (D J Wallace and R K P Zia, 1975) - https://iopscience.iop.org/article/10.1088/0022-3719/8/6/014/meta . The ...
3
votes
0answers
47 views

Correlation length amplitudes in Ising 2D model

I am reading the article about Universal amplitude ratios in the 2D Ising model (https://arxiv.org/abs/hep-th/9710019) by G. Delfino. I have a question about page 3 of the paper. For a magnetic ...
3
votes
0answers
37 views

Why does the RG group flow's linearization provide an eigenbasis at fixed points?

I'm reading Conformal Field Theory by David Sénéchal, Philippe Di Francesco, and Pierre Mathieu. Let $T$ be the map that generates the renormalization (semi-)group by taking couplings $J$ to $J'$ (...
3
votes
0answers
82 views

What happens to the dynamical critical exponent in the quantum-classical mapping?

It is well-known that one can, e.g., map the classical 2D Ising model to the 1D quantum Ising chain. Moreover, their critical points are related. Hence, if one is interested in critical exponents ...
3
votes
0answers
190 views

Phase diagram of the Z_N-invariant clock model

A well-known 1985 paper by Fateev and Zamolodchikov "Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points in Z_N-symmetric statistical ...
3
votes
0answers
90 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, $\psi^\dagger(...
3
votes
0answers
48 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 ...
2
votes
0answers
41 views

Relation between mean field critical point and RG critical point

In the mean field / Landau picture a critical point is where the potential of the order parameter changes curvature. E.g. the mean field potential of a scalar $\phi^4$ theory is $$\mathcal{L} = a t \...
2
votes
0answers
41 views

How to quantify frustration for spin models with long range interactions?

Consider the following Hamiltonian: $$ H=-\sum_{i\neq j}J_{ij}S_iS_j-\sum_i H_iS_i $$ where $S_i\in\{-1,1\}$, and the summed pair $i,j$ can be any two distinct indices (not necessary adjacent spins)....
2
votes
0answers
95 views

Difference between domain size and correlation length in ferromagnetic materials?

I am getting confused about different length scales in magnetic materials. I understand that the correlation length for a ferromagnetic materials is defined as <(s(x)−<(s(x))>)(s(y)−<(s(y))>)>...
2
votes
0answers
141 views

At what critical Reynolds number does vortex shedding begin?

In: "Fluid Dynamics", Chapter 3 (Turbulence), Section 26, Landau and Lifchitz analyze the problem of the stability of a steady flow past a body of finite size. The fluid is assumed to be ...
2
votes
0answers
74 views

Mean field critical exponents and the Gaussian approximation?

A while a go I asked this question on the difference between mean field theory and the Gaussian approximation. This question is related to that. The mean field critical exponents for the Ising model ...
2
votes
0answers
43 views

Relationship between the validity of mean field treatment and the strength of coupling/interaction

Mean field is a quite common treatment in studying phase transition and critical phenomena, although it neglects fluctuations. Imagine we have a Hamiltonian consists of free part and interaction part:...
2
votes
0answers
210 views

Kleinert's Variational Perturbation Theory

I've been reading Kleinert's book and have been very intrigued by the chapter on variational perturbation theory. Namely, Kleinert derives a very good strong-coupling approximation to the ground state ...
2
votes
0answers
81 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 ...
2
votes
0answers
355 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, ...
2
votes
0answers
214 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 term....
2
votes
1answer
121 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: "...
1
vote
1answer
64 views

What is the idea behind coarse-graining?

I don't think I fully understand the idea behind coarse-graining. I will elaborate. I was reading some lecture notes on statistical field theory and the text begins with some previous analyses on the $...
1
vote
0answers
65 views

Critical exponent mean field Ising model

I am given the following expression for the free energy: $$f = \frac{1}{2}r_0 m^2+um^4+vm^6,$$ where $r_0=k_B (T-T_c)$ with $T_c$ the critical temperature and $u=\frac{1}{12}k_B T$ and $v=\frac{1}{...
1
vote
0answers
18 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 ...
1
vote
0answers
78 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 ...
1
vote
0answers
70 views

How do we understand the results of $1/N$ or $\epsilon$ expansion beyond leading orders?

When we do $1/N$ expansions in, say, 2+1$D$ $O(N)$ models and try to extract all kinds of critical exponents from it, we get the following results for the scaling dimensions of various operators up to ...
1
vote
2answers
134 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 ...
1
vote
1answer
53 views

Trouble with critical expotent β

In the context of the Landau Theory of phase transitions, applying the mean field theory in an attempt to describe transitions such as the Nematic - Isotropic, the Landau energy density is given by $...
1
vote
1answer
91 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 ...
1
vote
0answers
98 views

What can happen on the “other side” of Berezinskii–Kosterlitz–Thouless (BKT) transition?

There is a generalized concept of Berezinskii–Kosterlitz–Thouless (BKT) transition in any dimension [not just in 2 dimensional classical system or 1+1 dimensional quantum system], such that the ...
1
vote
1answer
66 views

Compactification of Bosonic Closed Strings on $T^2$ and $T^3$

I am looking for a text to explain compactification of bosonic closed strings on $T^2$ and $T^3$ by focusing on its gauge groups enhancement. In fact, I want to know in each case ($T^2$ and $T^3$) how ...
1
vote
0answers
42 views

What's that theorem? All RG operators flow to directed percolation?

I can't for the life of me get this theorem straight. I can remember neither the name nor it's statement and would be grateful for anyone who wants to toss out some wisdom. It pertains to the ...
1
vote
0answers
90 views

Critical exponents from Ising free energy at zero magnetic field?

Consider the free energy of an Ising model $f(J,h,T)$, where $J$ is the coupling between neighboring sites, $h$ is the magnitude of a homogeneous external magnetic field and $T$ is the temperature. ...
1
vote
0answers
138 views

What is the anomalous dimension for two-dimensional multi-component spin systems?

My question is: What is the (predicted) anomalous dimension $\eta$ for the two-dimensional $n$-vector model (or $O(n)$ model)? Note: I am not looking for a derivation of $\eta$. A simple reference to ...
1
vote
0answers
16 views

State of the art results for locating critical points in 2D classical vertex models or 1D quantum spin chains

I'm looking for benchmarks for my own method, but I could not find an answer so easily. I've found so far: $\beta = 0.4407 \pm 0.0001$ for the 2D Ising model on a square lattice by Ghaemi, M., G. A. ...
1
vote
0answers
120 views

Bose-Einstein Condensation at higher critical temperature

The critical temperature $T_{c}$ of a Bose-Einstein Condensate is directly proportional to $n^\frac{2}{3}$, where $n$ is the density of the system which is to be condensed. The current $T_{c}$ for ...
1
vote
1answer
45 views

why when a circular superconductor cooled has magnetic filed?

i see in videos youtube that when a circular cooled about 200 kelvin it has some magnetic field around it,i think this Meissner effect is called , my question is how QM describe it??it is really ...
1
vote
0answers
147 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 ...
0
votes
0answers
41 views

Critical Mass Exponents in $d=3$

I'm just a Bachelor student, so forgive me if my questions seem too silly. I want to show the convergence of the critical exponents in the Renormalization Group equations when $d=3$. When I construct ...
0
votes
0answers
49 views

$CP^N$ model in Peskin & Schroeder problem 13.3

In Peskin & Schroeder exercise 13.3 question d, it is asked to perform an expansion of the term $$iS =-N.tr\left[\log\left(-D^2-\lambda\right)\right]+\frac{i}{g^2}\int d^2x \lambda $$ where $D_{\...
0
votes
0answers
19 views

Susceptibility with a complex order parameter

I want to compute mean-field exponents in a theory that has a complex order parameter. So, let's say I have $$ F=\int d\vec x \left[ a|\psi|^2 - \frac{b}{2}|\psi|^4\right] \equiv \int d\vec x A[\psi,\...
0
votes
0answers
35 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 ...
0
votes
0answers
44 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 $t=\vert T-T_c\vert/T_c$ ...
0
votes
0answers
27 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 ...
0
votes
0answers
47 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, ...