Questions tagged [phase-transition]
A phase transition is a change in the nature of a phase or in the number of phases of a system as a result of a change in the external conditions. Examples: melting/freezing, vaporization/condensation, ferromagnetic transition, superconducting transition.
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Open problems related with Berezinskii-Kosterlitz-Thouless phase transition
I was studying about BKT transitions and after some articles and books, I ended up with a question about the theory developed by the three scientists:
What open problems (if their exists) in current ...
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Coupling three Ising chains via an energy-energy-energy interaction
I want to note that this question is related to another one I asked involving just two chains coupled by an energy-energy interaction. I'm choosing to ask them separately because I suspect they may ...
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Isotropic classical model with a different phase transition than its anisotropic quantum limit
I have often heard that the isotropic ferromagnetically-coupled 2d classical Ising model and the quantum 1d transverse field Ising model have similar phases and the same universality class of their ...
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Coupling two Ising chains via an energy-energy interaction
Consider the transverse-field Ising model on a chain with periodic boundary conditions:
$$ H = -\sum_{i=1}^{L} \sigma_{i}^z \sigma_{i+1}^z + h \sigma_{i}^x$$
There's a phase transition at $h=1$, which ...
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Problem regarding open systems and a compression [closed]
Say we have a cylinder of height $h_0$ and transversal area $S_\perp$ filled with water vapour and covered by diathermic walls, as well as a mobile diathermic piston on the top, which is in contact ...
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Why does more ice melt slower than less ice?
I know that ice cubes that are larger melt slower because of their surface area. However, when you put more ice cubes in a cup, all the cubes melt slower than a cup with less cubes. I hope this makes ...
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Mapping a 1D quantum Ising chain to a 2-dimensional classical Ising system
Going through Ref. 1 (I'll stick with the book's equation numbering), I'm learning about the mapping of quantum systems into classical systems. First of all let me briefly recap notation and some ...
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A simple picture for the temperature vs density curve?
Consider $N$ particles interacting through a 6-12 Lennard-Jones pair potential (defined with particle radius $\sigma$ and energy barrier $\epsilon$) within a closed volume $V$ and evolving with ...
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Why do phase changes have to be isothermal processes?
I was wondering if someone can explain simply why phase changes are isothermal processes?
I am studying hydrology and some of our material about snowmelt has to do with phase changes and in this ...
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Why transparent object altering only the phase of light but not the frequency or amplitude? Is there exception?
I have learned the fascinating phase contrast microscope from Eugene's textbook optics that made transparent object become visible.
From page 647, he said that
In contradistinction, it is often ...
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Steam from a cup of coffee
I observed that, in winter there is more visible steam from a cup of coffee than in summer. Is there any phenomenon taking place here.
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Do liquids typically solidify under enough pressure?
Looking at the phase diagram of water,
it looks like increasing pressure of a liquid at any temperature eventually produces a solid. Liquid water becomes Ice VII at some pressure over 1 GPa and 350-...
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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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Quantum phase transition in condensed matter
I want to know that, for any spin-chains in condensed matter Physics like X-Y spin model, Kitaev model 1-D only in which degenerate point is critical point. Is it necessary that the critical points ...
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Determining melting point with equilibrium
A well known problem in thermodynamics is the determination of boiling points from the Van’t Hoff equation using the liquid-vapor phase equilibrium. When taking the temperature dependence of the ...
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Temperature and correlation with evaporation [closed]
If as water evaporates it carries energy with it and therefore there is a reduction in temperature, why does the temperature remain constant in the phase transition between liquid water and gas water?...
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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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What melts faster at room temperature, frozen salt water or frozen fresh water? [duplicate]
Suppose you freeze 2 ice cubes in the same freezer at -6F. One cube is pure water, the other is a saltwater cube. Take both cubes out of the freezer at the same time and put them into a room at say ...
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Why does the energy gap of sublattice-symmetric systems never close?
I am studying from this famous site some symmetries useful for topological quantum matter.
At some point, talking about the particle-hole symmetry, it states:
You can however notice that, unlike in ...
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Vaporization at constant volume
my question is the following: how much energy does it take to evaporate a liquid at constant volume?
For constant pressure, it’s very easy: Q = ΔHvap (Q in J/mol). However, the enthalpy of ...
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Is it possible for a droplet to condense in the middle (bulk rather than boundary) of the vapor without impurity?
As a rule of thumb, vapor condensation usually happens at the interface between the system and the heat reservoir. Now, according to my analysis below, it is the only way for vapor to condense, which ...
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Understanding the transfer matrix for a 1D Ising Model
I apologize in advanced for how trivial this question will come to many of you. I am in fact not a Mathematician nor physicist, just a math friendly Biologist who needs to understand the transfer ...
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Quantum Ising model phase transitions
In the classical Ising model, there are multiple ways to tackle questions regarding the existence of phase transitions. One way would be to look at spontaneous symmetry breaking of the order parameter ...
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Phase diagram of the Ashkin-Teller model for unequal intraplane couplings
The 2d Ashkin-Teller model is a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetric model consisting of two planes of Ising models on the square lattice with an interplane four-spin coupling:
$$H = -\sum_{&...
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Connection between thermodynamic potentials stability criteria and Gibbs potential minima in phase transition
As I was studying chapters 8 and 9 of Callen's books, I wondered about the following missing link.
In Chapter 8, a function of entropy S with respect to an extensive variable is shown:
It is argued ...
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Potential energy of a gas lighter than air
Here is the situation. Let's say I have have a mass of a given liquid and I heat it to create a gas. The gas has a lower density than air, so it will move higher and higer in the atmosphere. Then, I ...
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What effect does salt have on the boiling speed of water?
My question is the following:
I have two pots. Pot A and pot B. I fill both of them with 1l (litre) of water. Now I add a table spoon of salt into pot A. Which water is going to start boiling first?
I ...
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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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What is a dynamical description of phase transition?
In standard textbooks, it seems only giving a phenomenological description (like Landau paradigm, etc.). Is there a dynamical description？
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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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Potts model 1st order transitions and the sensitivity of $q_c=4$ to microscopic details
The ferromagnetic $q$-state Potts model describes a lattice of classical spins $\sigma=\{1,2,...,q\}$ and has Hamiltonian with nearest-neighbor interactions
$$
H = -\sum_{<ij>} \delta_{\sigma_i, ...
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When is a continuous phase transition in a translationally-invariant 2$d$ classical spin system not described by a CFT?
I'm trying to better understand when I should expect conformal invariance to emerge at a continuous phase transition.
I'm imagining classical, $q$-state spins living on the vertices of a 2d square ...
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Materials known to have higher density than Osmium at at high pressure and/or low temperature
This question is basically a modification of this.
It's well known that Osmium is the densest material you can find at room temperature and pressure. I am curious at higher pressures (and lower ...
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Will spinless particles with repulsive interaction solidify at high enough pressure?
I'm trying to understand better the formation of solids, such as when high pressure can induce a material to turn into a solid. In the following, I want to consider a toy model of $N$ spinless ...
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Relating phase transition with symmetry-breaking according to Landau Theory
I am trying to reproduce the results from this paper where they find out the expression for the Landau functional to be
$$\psi(x,t,p)=\frac{1}{4}(\frac{1}{x}+6x+px^3-4tx^2)$$
Now we plot Landau ...
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How to understand charge-$4e$ superconductivity?
Why might electrons exhibit a preference for forming a charge-$4e$ condensate, as opposed to the conventional BCS charge-$2e$ condensate? Could superconductivity potentially arise from pairings within ...
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Can real particles be created from a false vacuum spontaneously through decay?
Consider false vacuum decay.
Given the energy difference between the false to true,
Can this process lead to the creation of real particles as well as the vacuum bubbles?
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Chemical Potentials and Phase Changes [closed]
The Wikipedia article for the Helmholtz free energy has a derivation showing that if the volume and temperature of a system are kept constant, then
$$W \leq - \Delta F$$
Where $W$ is the work ...
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What are the two basic experiments to identify different phases in high $T_c$ cuprates systems?
what are the two basic experiments to identify different phases like antiferromagnetic, pseudogap, superconducting, strange metal and fermi-liquid in high $T_c$ cuprates systems like BSCCO and YBCO?
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Suscpectibility in Ising networks
I am struggling to find good references on how the susceptibility described phase transitions in Ising networks. First of all i struggle to find a good defintion for the susceptibility.
I understood ...
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What is the latent heat of melting for a everyday soda lime glass
This science direct article
https://www.sciencedirect.com/topics/chemistry/soda-lime-glass
States a particular type of glass (the most common one) and it's properties i was unable to find the latent ...
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How long does it take to boil water?
Consider a simple experiment, such as boiling water in a pot in your kitchen, is it possible to estimate the time needed for the water to boil based on elementary properties of water ?
In the physics ...
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Which symmetry is broken during an AdS black hole phase transition and does it lead to chaos?
I was going through this paper in which the authors state that :
In Landau theory, a continuous phase transition is associated with a broken symmetry.
The phase transition in a black hole system can ...
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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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Understanding the changing minima picture of phase transitions
Fix a simple $U,V,N$ system which is in contact with a temperature and pressure reservoir, so that the minimization of $G$ is the relevant criterion for equilibrium. This question is somewhat related ...
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Could someone explain this phase diagram to me?
I'm a litte confused by this diagram.
What does the "Diamond + metastasble Graphite" and "Graphite + metastable Diamond" regions mean? I mean at room temperature and Pressures, ...
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What is the reasoning behind Bragg-Williams approximation?
According to The book Statistical mechanics by Pathria, The Bragg-William approximation states that "the energy of an individual atom in the given system is determined by the (average) degree of ...
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How does adding heat cause helium-3 to freeze? [duplicate]
According to here at 3MPa helium-3 actually goes from liquid to solid at 0.1 kelvin, this is the complete opposite of how normal materials behave, how is this possible?
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Why does an eutectic liquid not change composition on solidifying?
Callen remarks that "If it is desired to have the solid precipitate with the same composition as the liquid, it is necessary to start with a liquid of" eutectic composition. Why is this so? ...
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On the Gibbs Phase Rule, and the structure of nonlinear equations
As far as I can tell, the Gibbs Phase Rule gives as a "law" the number of parameters which can be independently/a priori fixed when in an equilibrium with $r$ components and $M$ phases as
$$...
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