# 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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### Andrew's experiment

In Thomas Andrew's experiment, consider the dome shaped saturation region. If we increase the pressure at constant volume until we reach the critical point, why does the density of vapours rise and ...
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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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### 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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### 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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### 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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### What are phase transiton in different contexts?

I have come across the concept of phase transitions in various contexts. From simple phase transition between different states of matter like water to ice and so on, to phase transition in magnetic ...
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### Two methods to find critical exponents from renormalization-group equations

Consider a renormalization-group flow for a set of quantities $(x_1, ..., x_N) \equiv \bf x$, which can be written in the form ${\bf x}_{t+1} = {\bf F}[{\bf x}_t, T]$,where $T$ is the temperature. At ...
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### Aluminum critical current vs temperature fit

I have some data at different temperatures of Al's critical current (from 600 mK to 1.5K). Tc of Al is ~ 1.3. I am now trying to fit this data to a model to extract the theoretical critical current ...
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### If a salt solution heated under a pressure slightly lower than critical pressure will it boil?

8.8% NaCl solution for example have a critical point of 450°C under 423 bar pressure. If we heat such solution to same temperature under slightly lower pressure i.e. 420 bar should it will boil or it ...
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### System-size dependent phase transitions

I noticed that some physical phenomena require a system of size above some critical value to be observed. Two examples I know are: For a single-atom gold wire, there is a critical number of atoms to ...
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### 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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### What is the difference between these three definitions of specific liquid heat capacity?

This is an excerpt from the page 6.18 of book "Properties of gases and liquids, 5th ed". I can figure out the difference between the first one C_pL with other two, but cannot distinguish latter two, ...
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### spontaneous symmetry breaking within critical phases

There are many examples of the spontaneous symmetry breaking in discrete symmetries which result in the gapped phases, such as dimerization phase of the quantum antiferromagnetic spin-1/2 chain which ...
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