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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Why is the energy of a vortex in a superconductor finite?

I just had a glimpse of the Ginzburg-Landau theory of superconductivity. I am surprised that that the energy of a vortex is finite. This is surprising because as far as I know, in superfluids, the ...
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Critical exponents and scaling dimension

It is often stated that the scaling exponents, e.g. $\alpha$ and $\beta$, of the critical 2D Ising model are related to the scaling dimensions $\Delta_{\sigma}$ and $\Delta_{\epsilon}$ of the ...
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Could 2D critical quantum system be described by 3D conformal field theory?

It is well known that 1D quantum critial systems are described by 2D cft. Could 2D critical quantum system be described by 3D conformal field theory?
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Divergent or not? the heat capacity at the lambda point

In Kerson Huang's book (2nd edition, page 309), it is stated that at the lambda point, the heat capacity diverges logarithmically. But, in wiki, it is stated that it is finite. https://en.wikipedia....
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How many universality classes are there in the universe?

There are more-than-we-can-count number of phases in the universe, all described by their interesting symmetries. But what about universality classes? Is the number just as big? Ising, Heisenberg, XY ...
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How to get the binodal and spinodal from an equation of state?

We know that the Flory-Huggins polymer solution theory predicts a upper critical solution temperature. In their approach, FH find out the free energy of mixing, $F(\phi)$. This is done in a mean-field ...
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Is central charge related to symmetry?

I am currently reading the paper "Theory of finite-entanglement scaling at one-dimensional quantum critical points" by Pollmann et. al. and I am trying to understand the central charge in ...
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Question about the so-called upper critical dimension

It is often said that above the upper critical dimension, the mean field theory is correct. What is the precise meaning of this statement? Let us be specific and consider the $d$-dimensional Ising ...
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Is the transition from laminar flow to turbulent flow a kind of phase transition like those in condensed matter?

From the laminar flow to turbulent flow, is it a kind of phase transition? If so, what is the critical point? And what about the correlation length behaviours and fluctuation? Any critical exponents? ...
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Lower bound on the spectral gap in finite size critical systems with locality

Local quantum systems tuned to criticality are gapless in the thermodynamic limit. The rate at which the ground state spectral gap approaches zero as the system size $L \rightarrow \infty$ carries ...
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How to understand the notion of critical temperature in thermodynamics?

I just want to verify my understanding of the notion of critical temperature of fluids, because the more I read about it in the literature I become more and more confused. My main clue for ...
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"Quantum" hyperscaling relation from a Renormalization Group (RG) viewpoint

Through the RG method, one can obtain the hyperscaling relation between the critical exponents of classical second-order phase transitions: \begin{equation} 2-\alpha=\nu d \end{equation} In the case ...
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What is the difference between charge density wave (CDW) and charge ordering (CO)?

I am suffering with the terminology of condensed matter physics. When I read papers about strongly correlated electron system, sometimes I see the words "charge density wave" (CDW) and "...
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Power-Spectrum for Self-Organised Criticality

In 1987 Bak, Tang and Weisenfeld authored a paper (link) on Self-Organised Criticality, on how minimally stable self-organised systems propagate the perturbations it is subjected to, scale-freely - ...
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What is the order of the transition for a 2D Ising model?

I have been running around the block trying to find answers for this question, and I keep running into caveats. So, I just want to write down the list of things I want to know: Given that the order ...
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First-order phase transition in the Ising model?

I am doing a simulation of the 2D Ising model with a Monte Carlo algorithm. I think that the model should exhibit a second order phase transition at $\beta=\beta_c$, but when I try to plot the ...
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How can I find the critical dimension for the Blum-Capel model near the tricritical point in mean field theory?

I believe that I have found the critical dimension for the critical temperatures on the critical line (that is, where the second order phase transition occurs), which is $D=4$. This is because the ...
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Simulation time for Ising model of large systems

I have tried to run simulation for Ising model of large-size square lattices at the critical point. Mostly I use Python optimized with numba decorator for $L=256$ it takes approx 2.5 min with ...
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At the critical point, is Kramers-Wannier duality a unitary symmetry of the model?

I have in mind the transverse ising model and its (self-dual) generalizations, such as $$H_{TI} = \sum_i \sigma^z_{i}\sigma^z_{i+1} + h \sigma^x_{i}$$ and $$H_{SDANNI} = \sum_i (\sigma^z_{i}\sigma^z_{...
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Two lines of critical points described by CFTs with different central charges intersect. What happens?

There is a lovely set of two-parameter spin chains that can be mapped to quadratic fermions and studied quite exactly: $$H = -\sum_{i} \frac{1+\gamma}{2}\sigma^x_i\sigma^x_{i+1}+\frac{1-\gamma}{2}\...
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Phase space of Ising minimal model + deformations

Consider the Ising field theory, a conformal field theory in 2 dimensions which corresponds to the minimal model $\mathcal{M}_{4,3}$ and it's perturbations by the relevant operators $\epsilon, \sigma$ ...
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Entanglement universality at criticality

In $(d+1)$-dimensional quantum systems described by conformal field theories at criticality, I have been under the impression that the entanglement entropy is described by a non-universal area law ...
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Log-law entanglement with large central charge contradict bounds on the entanglement entropy

I am trying to learn more about entanglement entropy in large but finite-size systems at critical points. I am still relatively new to conformal field theory, so it is not unlikely I have ...
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Terminology for scenario when energy of system $E(\theta_1,\ldots,\theta_k)$ with $k$ real parameters, is minimum whenever $\theta_1=c$ (fixed value)

Disclaimer. I'm not a physicist. Consider a physical system whose "energy" $E$ is a function of $k$ real parameters $\theta = (\theta_1,\ldots,\theta_k) \in \mathbb R^k$. Let $E_{\min}$ be ...
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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 ...
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What is a correlation length? [duplicate]

What is a correlation length? I encountered this term in my space physics lecture, in the context of the "correlation length of the magnetic field magnitude," but I am not sure what does it ...
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Connection Between Renormalization Group and Phase Transitions

I have a couple of questions on the relation of RG and phase transitions. I've heard in many sources that the theory of most transitions (excluding novel phase transitions like Quantum Critical ...
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Doubts in Derivation of Critical constants, for real gases

I had been reading about critical constants for real gases, and was been asked (in a test) to derive the constants from Van der Waal equation for real gases. So following was question: The Van der ...
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Differences between critical temperatures in Ising Model

The critical temperature $T_c$ for the 2D square lattice ferromagnetic Ising Model is known exactly to be $$T_c=\frac{2}{\ln(1+\sqrt{2})}$$. For other geometries, say, a 3D cubic lattice or a 2D ...
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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 ...
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How to generate a PDE from a discrete equation in a rice-pile like model?

I am reading Noise and dynamics of self-organized critical phenomena by Albert Díaz-Guilera Here, on an extension of the rice-pile model by Bak et al demonstrating self-organized criticality. Equation ...
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Transitions in Ising lattice gauge theories in 3+1 dimensions

What is known about the character of the transition (apart from the self-duality of the model and its self-dual point marking the transition point) in the Z2 lattice gauge theory in 3+1 dimensions?
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Does scaling appear on a phase boundary/first order phase transitions, or it is only reserved to critical points?

In statistical mechanics people talk about scaling laws and critical phenomenon, and one of the textbook examples brought up is the liquid-gas critical point. But in contexts of Superconductivity and ...
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First and second order phase transition classificiation and scope of Landau theory

I am puzzled by the definition of continuous and first-order phase transitions and the use of Landau theory. I think I am lost in technicality. In the phase diagram below the critical point, we have ...
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How much Curie temperature is obtained according to the Stoner model?

In Stoner model for itinarant ferromagnetism, the spin ordering of electrons is caused by the Coulomb interaction $U$ for onsite repulsion leading to the reduction of total energy against to the ...
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Scale invariance beyond the critical point

Using Anderson localization as an example, I understand how scale invariance comes into play at a critical point - at a critical point, the localization length $\xi$ (the average "radius" of ...
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Didactic model for tipping dynamics [closed]

I would like to know if there are some toy models that describe a system dynamic from ecology or earth science with some feedback loops (eg. ice-sheet cover, rainforest-savanna cover, permafrost ...
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Mermin-Wagner and superconductivity

Why can superconductivity exist in 2D since Mermin-Wagner should forbit it? This question was asked here before, but I don't think anyone gave a satisfactory answer, so let me revisit it. I have read ...
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Are quasiperiodic critical points described by non-unitary CFTs?

In a continuous phase transition driven by quenched disorder, the conformal field theory (CFT) describing the critical point often seems to be non-unitary. An example would be the Anderson ...
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Dimensionless vs. dimensional RG-Flow equations

When one writes down RG-Flow equations for any theory, at some point one encounters statements like "It is useful to properly rescale the above exact flow equations and rewrite them in ...
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Phase transition vs. critical phenomena

Just trying to get some clarity in terminology: is phase transitions synonymous with critical phenomena? At the first glance they mean the same thing, but I am not sure whether phase transitions ...
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Why are critical points of classical systems described by quantum conformal field theories?

So, the question is pretty much in the title: why are critical points of classical systems described by quantum conformal field theories? I get that schematically, conformal symmetry (or rather scale ...
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Is there actually a one-to-one correspondence between a given central charge $c<1$ and a given universality class?

I'm just starting to learn about conformal field theory, with an aim to understand critical exponents in terms of conformal fixed points. I see, in multiple locations, the claim that a central charge $...
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Critical Field outside the Meissner limit - derivation

In Tinkham's "Introduction to Superconductivity" Second Edition, Chapter 2.2.1, the author states that ... the superconducting state becomes energetically unfavorable above the magnetic ...
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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 ...
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Ratio of atomic and molecular hydrogen depending on temperature and pressure

I am interested in all kinds of theoretical/experimental results about the ratio of atomic and molecular hydrogen, in particlular in the high pressure (>10 GPa) and high temperature (~5000 K) ...
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Delta functional representation in response field formalism

A general way of obtaining a field-theoretical description of Langevin dynamics is via the Martin-Siggia-Rose (MSR) response fields. This is essentially just representing the identity - up to some ...
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Is landau theory for phase transitions valid only for "order to disorder" phase transition?

In the landau theory we assume order parameter that is equal to zero at $T>T_c$ and none zero at $T<T_c$ wich is valid only for order to disorder phase transition according to my understanding. ...
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Rushbrooke critical exponents inequality general case

According to wikipedia https://en.wikipedia.org/wiki/Rushbrooke_inequality this inequality true for magnetic systems. but what about PVT systems? or is it true in general? I tried to look for a ...
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How do I actually derive the Griffiths inequality for critical exponents? [closed]

The Griffiths inequality for critical exponents says $$\alpha+\beta(1+\delta) \geq 2$$ I have looking for the internet for a full derivation but couldn't find anything.
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