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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Particular Ising Model of Cellular Automata Shows Mathematical Properties [closed]

I have written a cellular automaton that shows very unusual properties connecting the critical point of 2D square-lattice Ising model and the golden ratio. My question is, is the algebraic method ...
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Ferromagnetic/Paramagnetic Phase Transition in a Non-Zero External Magnetic Field

I'm new to condensed matter theory, especially spin-glass systems. I understand that the Ising model exhibits a Phase Transition when there is no external magnetic field (h=0). And that at the ...
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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 ...
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Critical exponent relation for neural avalanche dynamics

I am trying to understand the origin of equation (4) in this paper. Per the arguments of Touboul and Destexhe, a power law distribution for avalanche size and duration, as well as observed data ...
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59 views

How to find the critical exponent of some directional dependent correlation length?

I am working on a two dimensional anisotropic system with correlation length diverging with different critical exponent in different directions. And I am wondering if there is any theoretical ...
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378 views

Ising model Monte Carlo simulations in 4D and 5D

I'm going to be simulating the Ising Model in 4D and above to calculate spin-spin correlations and critical exponents and am wondering how to tackle this algorithmically. For example, in 1D, use an ...
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28 views

Critical supercurrent

What is meant by the concept of critical current when talking about superconducting phase diagrams and transitions? How does this relate to critical field and temperature? Thanks
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Ising model 1D spontaneous magnetisation

What does it mean to 'compute the spontaneous magnetisation'? According to wikipedia: 'Spontaneous magnetization is the appearance of an ordered spin state (magnetization) at zero applied magnetic ...
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33 views

Three point correlation function 2D Ising model

What is the expected behaviour of the three point function $<\sigma_i \sigma_j \sigma_k>$ of the Ising 2D model at the critical point where conformal symmetry is valid? Do they have a power-law ...
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101 views

Various questions on renormalization in lattice systems

Forgive the long, multi questioned-question. The setting of this question is inspired by this answer. Consider some theory on a lattice, for example the 2D $0$-field Ising model $$H=-K\sum_{\langle i,...
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144 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))>)>...
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Renormalization Group Flows

In the Renormalization Group flows, why there are two fixed points: Gaussian and Wilson Fisher and does the Gaussian Fixed point describe the critical behaviour of the system?
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What is a good definition for what this article talking about when it refers to “Universal Physics”?

I was puzzled when I read "Precise measurements find a crack in universal physics by Ingrid Fadelli" (Phys.org, Jan. 15, 2020). The article has some vague statements in the opening paragraphs about "...
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36 views

Approximately how long after forming a critical mass of fissionable material does it explode?

Just making up some quantities of variables to reduce the “depends” answers/comments. Given, say: enriched uranium mass of 1.5 x critical mass spherical shape brought together “quickly” (a few ...
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Yang-Lee article on phase transition (1952): possible problem in lemma demonstration

I'm studying the first article of Yang-Lee on phase transition C.N.Yang and T.D.Lee, Physical Review, ”Statistical Theory of Equations of State and Phase Transitions. I. Theory of ...
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135 views

Question about Landau theory of Phase Transitions

The landau theory makes a mean-field approximation on the order parameter, which assumes that there are no fluctuations in the value of the order parameter at different sites (neglects the effects of ...
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130 views

Calculating Dynamic Critical Exponent in Continuum Field Theories

For a critical point controlled by $\delta$ described by a correlation length $\xi$ and a correlation time $\xi_\tau$, the critical exponent $\nu$ and the dynamic critical exponent $z$ is defined as $\...
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Book recommendation for statistical physics

Before I start a PhD in Quantum Information I would like to study a bit of statistical physics. In particular I am interested in superfluids, critical phenomena, topological phases of matter and all ...
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Order parameter to quantify clustering?

I have a 1D system containing $N$ particles having positions $\{x_1(t),x_2(t),\dots,x_N(t)\}$ in a box of size $L$ with periodic boundaries. The number of particles is conserved. The dynamics of the ...
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1answer
90 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 $...
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150 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 ...
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Some Questions about the Critical Point

I'm currently trying to understand the physics of phase transitions and I'm having a hard time doing that. First of all, the discussions on the topic seem to be confusing and there is no methodical ...
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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 ...
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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 ...
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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 $v=\frac{1}{...
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$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_{\...
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Could the Odderon intercept be equal to $\alpha_\mathbb {O}(0)=0.813$? [closed]

The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space): $$\beta=\beta'=0.813(9)$$ $$\nu_\perp=0.584(5)...
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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,\...
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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 ...
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187 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 ...
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58 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, ...
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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 ...
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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 $t=\vert T-T_c\vert/T_c$ ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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109 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?...
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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 ...
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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, ...
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159 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, ...
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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 ...
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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 ...
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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 ...