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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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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 ...
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Role of the natural temperature scale in the anomalous dimension of the renormalization group

In David Tong's lecture notes on statistical field theory, the concept of anomalous dimensions is introduced by considering the scaling of the correlation function $$\langle \phi(\mathbf{x}) \phi(\...
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Ising model in a magnetic field (phase transition?)

I have some questions regarding the Ising model in the presence of a magnetic field which is non-uniform. Let us define the Ising Hamiltonian on a $d-$dimensional lattice, $$ H = -\frac{1}{2} \sum_{i,...
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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 ...
Dirac's delta's user avatar
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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 ...
Ibrahim Khalil's user avatar
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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 ...
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Can the Wilson-Fisher fixed point be reached from the massless $\phi^4$ action?

Most textbooks and papers work out the derivation of the Wilson-Fisher fixed point for $\phi^4$ starting from the massive action (in Euclidean space) $$S = \int d^d x \biggl( \frac{1}{2} \partial_\mu \...
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Anomalous dimension must be positive in Ginzburg-Landau $\phi^4$-like theories?

I am trying to understand/find the argument behind a claim made in this paper (page 3, column 1): that the anomalous dimension/exponent $\eta$ of a continuous phase transition in Ginzburg-Landu $\phi^...
bbrink's user avatar
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Spontaneous symmetry breaking in phase transitions

I don't really understand the concept of spontaneous symmetry breaking in phase transitions. From my understanding of how spontaneous symmetry breaking works I need to find the ground states of a ...
Alex's user avatar
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Book recommendation for CFT in condensed matter theory

I've been looking for sources about conformal field theory (CFT) applications in condensed matter theory (CMT) like bosonization, critical phenomena, and QFT anomalies. I have studied CFT from ...
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Cluster Monte Carlo algorithms for $n$-body interactions

Suppose I wanted to perform a Monte-Carlo numerical simulation of an Ising-like model, with a Hamiltonian of the form $$ -\beta H = J \sum_{\langle i j \rangle} \sigma_i \sigma_j + g \sum_{ijk\ell \in\...
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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, ...
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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 ...
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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 ...
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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 ...
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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 "...
Mitchell Porter's user avatar
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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?
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3-dimensional 3-state Potts model critical temperature

I was given that the free energy per lattice site of the 3-dimensional 3-state Potts model in the mean field approximation is $$f\equiv \frac{F}{\text{# sites}} = \sum_{k=0}^{2}(-3Kx_k^2 + \frac{1}{\...
slowspider's user avatar
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1 answer
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Critical Temperature of a Bose-Einstein Condensate

I found that most sources and derivations of a relationship between the fraction of bosons in the ground state and normalised temperature are given as $$\frac{N_0}{N} = 1-\left(\frac{T}{T_C}\right)^{\...
Jack Tiler's user avatar
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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 ...
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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 ...
sangara's user avatar
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3 answers
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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?
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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 ...
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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, ...
2 votes
1 answer
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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 ...
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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 ...
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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 ...
QFTheorist's user avatar
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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 ...
ShoutOutAndCalculate's user avatar
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Combinatorics in $\lambda \phi^4$ theory and critical exponents

I am trying to understand critical phenomena from the perspective of Statistical Mechanics. The interacting term in the $\lambda \phi^4$ scalar theory is usually (but not always) multiplied by $\frac{...
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Reference for critical exponents in a non standard derivation

I'm currently preparing an individual project about Landau theory of phase transitions. I think I understand well enough the standard procedure: expand the free energy as $F(P, T, \phi) = F_0(P, T) + ...
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Why is a critical point defined as a stationary inflection point?

In the analysis of a van der Waals equation of state, it's quite clear that the temperature and pressure at which $$ \left( \frac{\partial p}{\partial V} \right)_T = 0\\ \left( \frac{\partial^2 p}{\...
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7 votes
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Ising model phase transition when external magnetic field is non-zero

In the Ising model, when the external magnetic field is absent, it has a second order phase transition, because there is a discontinuity in the magnetic susceptibility vs Temperature, T (and magnetic ...
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3 answers
248 views

Is it physically possible to bring water to its critical point?

I've been thinking about the critical point of water, which has three distinct and specific properties: critical temperature, critical pressure, and specific critical volume. However, when I draw a PV ...
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Transfer matrix for the calculation of average spin in ising model

Background Consider 1-D Ising model of n lattice points with periodic boundary condition, $\beta H(\sigma_1,\sigma_2,...,\sigma_N) = -\sum_{i=1}^nk(\sigma_i\sigma_{i+1})-\sum_{i=1}^n\sigma_i$ $k=\beta ...
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What is the physical meaning of critical points in black hole thermodynamic topics?

In black hole thermodynamic topics, the critical points sometimes calculate. They are introduced in different types and calculated in conventional forms. Recently, in thermodynamic calculations, these ...
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2 answers
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Is renormalization different to just ignoring infinite expressions?

Looking into textbooks, I got the impression in renormalization perturbation theory one adds counterterms to the Lagrangian to cancel terms (usually integrals) that are infinite. My question is, could ...
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Is the lattice spacing $a$ a dangerously irrelevant parameter?

Near a renormalization group fixed point, we can perform a scale transformation of length $L' = b^{-1} L$. In this case the relative lattice spacing should transform as $a' = b^{-1} a$. After $n$ ...
gene's user avatar
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Correlation function in the critical two-dimensional Ising model

Fifty years ago, McCoy and Wu in their book The Two-Dimensional Ising Model formulated a hypothesis about the correlation function in the critical two-dimensional Ising model. According to this ...
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Why is the supercritical fluid region a perfect rectangle?

The melting, sublimation and evaporation curves are all non straight lines in a (p,T) phase diagram, while the curves that divide liquid/gas regions from supercritical fluid region are perfectly ...
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Analyzing a Kawasaki-evolving Ising model? (conserved-order-parameter Ising model)

Focusing on 2D in further text I am struggling to understand how the conserved-order-parameter Ising model (also known/reached through Kawasaki algorithm) shows criticality and also how it can be ...
dasolina's user avatar
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Extra term in $2+\epsilon$ expansion of sigma model

I'm working through David Tong's notes on Statistical Field Theory, in particular the $2+\epsilon$ expansion of the sigma model with free energy $$F[\vec{n}]=\int d^dx \frac{1}{2e^2}\nabla\vec{n}\cdot\...
acernine's user avatar
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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 ...
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4 votes
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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 ...
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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 ...
Níckolas Alves's user avatar
2 votes
1 answer
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 ...
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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 $$Z=\int D\theta(x)\,exp(-\frac{K}{2\pi}\int d^{2}x\,(\nabla_x\theta)^2),$$...
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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 ...
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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 ...
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Order Parameter, Phase transition

Is order parameter for a phase transition is unique? Is it always true that in one phase order parameter have zero value and in another phase it has non zero value? Is there any standard rules for ...
Sita Chettri's user avatar
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Goldstone Bosons and Criticality

In the presence of spontaneous symmetry breaking of a continuous symmetry, there are massless goldstone bosons. However, they are not treated in the discussions of critical phenomena. Naively I would ...
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