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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.

The term critical phenomena refers to the behavior of physical systems close to a critical point. Well-known examples are the critical temperature of a ferromagnetic transition and the critical $(P,T)$ point of a liquid-gas transition.

The term critical phenomena is thus usually associated to continuous (second-order) phase transitions. Examples of critical phenomena occurring during second-order phase transitions are:

  • Dynamical slowing down
  • Divergence of the correlation length
  • Emergence of scaling laws
  • Power-law divergence of physical quantities (like the magnetic susceptibility $\chi$ in a ferromagnetic phase transition)
  • Ergodicity breaking
  • Emergence of fractal structures
373 questions
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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 transition exhibits a discontinuity in the first…
N. Virgo
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Examples of important known universality classes besides Ising

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical systems, textbooks seem to always end up with the…
Steven Mathey
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What is the definition of correlation length for the Ising model?

The correlation length $\xi$ is related to critical temperature $T_c$ as $$ \xi\sim|T-T_{c}|{}^{-\nu}, $$ where $\nu$ is the critical exponent. Is this the formal definition of correlation length? If not, what is the formal definition of…
cosmicraga
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Are there classical infinite order / continuous non-symmetry breaking phase transititions besides Berezinskii-Kosterlitz-Thouless (BKT)?

At the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, the singular part of the free energy behaves as $\xi^{-2}$, where $\xi \propto e^{c/\sqrt{T-T_c}}$ (with $c>0$) is the correlation length. Hence $\xi$ has an essential singularity at…
Eruvaer
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What is the relation between non-local order parameters and topological phases?

I know of several definitions of phases of matter: The first is the "old" one, Landau theory and symmetry breaking. In this definition we pick a local order parameter $m$ (as far as I can tell this is quite vaguely defined). If the state had the…
user2723984
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Why do spin correlation functions in Ising Models decay exponentially below the critical temperature?

I'm trying to form a better understanding of the 2D Ising Model, in particular the behaviour of the correlation functions between spins of distance $r$. I've found a number of explanatory texts that seem to indicate that at both above and below the…
Suh doh nimh
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Fluids with critical point at ordinary temperature and pressure

Are there any fluids with critical point near STP or that are supercritical at STP? If not would it be feasible to design a molecule for a substance with critical point near STP using theoretical/computational methods? Update @Diracology and…
Daniel Mahler
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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: "Why does the correlation length become…
P. C. Spaniel
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Are the first order phase transitions always associated with a latent heat?

Is the first order ferromagnetic transition below the critical temperature associated with latent heat? For example, the transition of ferromagnetic configuration with all its spins aligned up to a ferromagnetic configuration with all its spins…
SRS
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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 magnetic field) $Z^{(N)}(t, h)$, where $t$ is…
user3657
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Why correlation length diverges at critical point?

I want to ask about the behavior near critical point. Let me take an example of ferromagnet. At $T < T_c$, all spins are aligned to the same direction thus it is in the ordered state, scale invariant, its correlation length is effectively infinite.…
john
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What leads to the existence of critical temperature?

We know that $T_c$ is the temperature above which no amount of pressure could force a gas to liquefy. But why is this? Somehow I don't buy the point that the gas molecules exert too much pressure back to get close and turn into a liquid. If we had…
cst1992
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If boiling of water involves change in internal energy, then why does the temperature remain constant?

According to the first law of thermodynamics, $$\Delta Q=\Delta W+\Delta U$$ Considering boiling of water to be an isothermal process, $\Delta U$ should be zero, but then my textbook says: "we see that most of the heat goes to increase the internal…
Chahak
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Is Wilson-Fisher fixed point unique?

It is well-known, that in $\phi^4$ theory in 3d there is interaction fixed point: $$ S_{\Lambda} = \int d^dx \left[\frac{1}{2}(\partial_i \phi)^2 + \frac{1}{2} \mu_0^2 \phi^2 + \Lambda^{d-4} \tilde{g}_0 \phi^4 \right] $$ From equations of…
Nikita
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Non-uniqueness of the Order Parameter and its Critical Exponent

In the theory of phase transitions, an order parameter is usually defined as some quantity which distinguishes the two phases of the system by being zero in one phase, and non-zero in the other (see e.g. this and this question). This definition has…
Sahand Tabatabaei
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