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bose einstein phase transition

From Carter's book Thermodynamics and Statistical Mechanics, the partition function of a bose-einstein gas in $d$ dimensions is $$ \ln(Z) = ...
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Correlation length during phase transitions in early Universe

During phase transitions of the second kind topological defects may form on the bounds of two areas separated by correlation length. In early Universe during phase transitions correlation length ...
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0answers
34 views

What is the viscosity difference between a solid and a liquid

The pitch drop experiment, for example, shows bitumen as a liquid, even though it appears to be a solid, and then there is the "glass: solid or liquid" debate. Is there a numerical value in viscosity ...
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28 views

What is crossover?

It is known that EW and QCD phase transitions in SM are so-called "crossovers". What is the difference between crossover and phase transition of the second kind?
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27 views

Topological configurations and phase transitions

It is known that topological defects might appear only during phase transitions of the first kind, while continuous transitions of the second kind and crossovers don't product them. How to explain ...
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42 views

Axion domain walls and QCD phase transition

Now it is known that QCD phase transition corresponds to crossover. This it seems that no topological defects is produced during phase transition. Do axion domain walls arise during QCD phase ...
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18 views

Question on distinct phases through spontaneous symmetry breaking.

If I have a many-body Hamiltonian that is invariant under the representation of a certain group $G$ i.e [H,U(g)] = 0, how many phases does can exist through spontaneous symmetry breaking (SSB) of this ...
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40 views

The bounds of axion domain walls are axion strings?

There are two phase transitions which are important for the axion physics. The first one is Peccei-Quinn phase transition, during which axions arise. The second one is QCD phase transition, at which ...
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2answers
41 views

Gibbs phase rule and degrees of freedom at the triple point / triple line

The Gibbs phase rule tells me that at a substance's triple point, where there are 3 phases in equilibrium, there should be 0 degrees of freedom. Based on my understanding, that means there should be 0 ...
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1answer
147 views

Why does hitting a cold bag of water freeze?

About 24 hours ago, I bought a box of 30 pieces water ice. I put them in the freezing compartment and when I came from work I was expecting a nice chilling ice. But when I opened the freezer, I saw ...
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0answers
10 views

Why do some rectangular lattices turn into cubic lattices upon heating?

Lattices that are rhombic or rectangular have been known to expand in the two shorter axes directions when heated until a cubic structure is reached before expanding linearly in all directions. Why is ...
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2answers
118 views

Phase transition without the Peierls' counter argument

Is there any proof of the existence of phase transition in models of statistical mechanics of the Ising type models without using the Peierls' argument and its variations? By models of the Ising ...
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1answer
29 views

What will happen if 0°C water is slowly added into a vacuum container adiabatically/isothermally?

I have thought about this question for a while. If adiabatically, according to the phase diagram, I think the water will first evaporate with temperature decreased because of the 0 pressure. I don't ...
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1answer
55 views

What are the symmetry criteria for continuous phase transitions in Landau theory?

My understanding is that within Landau theory, a continuous phase transition is only possible if certain symmetry rules are satisfied. (These rules represent necessary but not sufficient conditions ...
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28 views

Specific Heat of Liquid Helium

At the lambda point, the specific heat of Liquid Helium diverges. After searching for a curve, I've found only measured curves. Is there a theoretical curve for this transition?
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1answer
35 views

What happens at lambda point?

When Boson gas approach lambda point (no matter from superfluid side or liquid side),the heat capacity tend to diverge, doesn't this mean that we can never drive the gas through lambda point?(cause we ...
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0answers
23 views

What is the difference between primary and non primary order parameter?

I found that antiferomagnet has non-primary order parameter and I don't know what is the main feature of (non-)primary order parameter?
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0answers
28 views

One question about critical exponents for first order transition free energy [closed]

I've got a problem to calculate critical exponents for theory given by Landau free action: $$ \tag 1 L = L_{0} - \frac{1}{2}(\nabla m)^{2} + atm^{2} + dm^{3} + bm^{4} - hm, $$ where $$ -\infty < ...
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1answer
18 views

Deformation in the nematic phase of a liquid crystal survived in solid state

Does anyone know if I cool a liquid crystal with a deformed nematic phase quickly it will preserve the deformation in the crystal lattice? I didn't never see that in classical books on liquid ...
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0answers
31 views

What do physicists mean with “classical critical behaviour”?

What do physicists mean with "classical critical behaviour"? As far as I am concerned it should be "power law behaviour" of some quantity close to the critical point but I ask here to be sure.
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Transformation Diagrams for Ceramics

So, in the field of metallurgy, there are a few varieties of phase diagram that are used to predict the post-processing characteristics of alloys. These include Time-Temperature Transformation ...
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16 views

EW phase transition and baryogenesis

There are three Sakharov conditions of baryogenesis: CP symmetry violation. Baryon number conservation violation. Thermodynamical equilibrium violation. In SM the first one is satisfied by CKM ...
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1answer
52 views

Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition?

The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the ...
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1answer
51 views

Helmholtz Free Energy vs Gibbs Free Energy in Landau Theory

When I was studying thermodynamics potentials for the first time, I learned that keeping the pressure and the temperature constant, the Gibbs Free Energy is a minimum, also, if we maintain the ...
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227 views

Is there a definite boundary between a powder and a fluid?

Given a powder of solid substance what will happen if we make the granules smaller and smaller mechanically? Will this eventually make a liquid or gas from the powder? Can there be gaseous substanse ...
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1answer
48 views

Paramagnetic/ferromagnetic transition under a magnetic field

The paramagnetic/ferromagnetic phase transition is an archetypal example of a continuous (or second-order) phase transition. When the temperature $T$ approaches the Curie temperature $T_c$, the ...
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2answers
93 views

Good layman definition of the critical point(phases) and supercriticality

I've heard of this point among others, but never really got what it meant. Wikipedia makes one's head spin. The only thing I picked up is that it occurs between liquid and gas, and displays ...
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1answer
55 views

Is the Landau Free Energy U-TS or βH?

I'm having a hard time figuring out the physical meaning of the Landau Free Energy density: $$f(\phi,\nabla\phi,T) = \frac{1}{2}|\nabla\phi |^2 + \frac{a(T-T_c)}{2}|\phi |^2 + \frac{b}{4}|\phi |^4$$ ...
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5answers
160 views

What compounds or elements only have one phase or two phases?

Wood appears to be one. I think gases like helium and hydrogen cannot exist in the solid state under normal pressures, correct? And why do those "phase cheaters"-- those elements/compounds which ...
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0answers
58 views

Why the non-analyticity of free energy function implies phase transition? And what's its connection with other 'higher level' free energies?

I have seen 'free energy' arising from several contexts in very different forms, and each contains different amount of information. For example free energy is defined as the logarithm of the ...
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1answer
61 views

Universality classes

I would like to ask about the universality classes. I know that these are the statistical models which describes different phase transitions with different critical exponents. But I would like to know ...
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1answer
36 views

Explanation of relationship between pressure and poiling point of water [closed]

Explain how an increase in pressure elevates the boiling point of water, while reducing the pressure depresses the boiling point?
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1answer
63 views

Ising model scale invariance

Could someone help me and explain what is the connection between divergence of the correlation length, and the scale invariance. So why will in the critical point the system show scale invariance if ...
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0answers
22 views

Singularities across the critical isotherm in Landau's phenomenological theory of phase transition

Why don't we encounter any singularities when crossing the critical isotherm when $h \neq 0$ or $m\neq0$, where $h$ is the ordering field and $m$ is the order parameter.
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How does the specific resistance / conductivity changes, when melting metals?

According to standard school models, the specific resistance (or conductivity) depends on the movability of the charges. In a metal lattice, some electrons can freely move and are only hindered by ...
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5answers
479 views

How to understand singularities in physics?

The question is probably two-folded and I will try not to make it too vague, but nonetheless the question remains general. First fold: In most physical laws, that we have analytic mathematical ...
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0answers
48 views

Landau theory of phase transation

In his article http://www.ujp.bitp.kiev.ua/files/journals/53/si/53SI08p.pdf, Landau defines probability distribution $\rho$ which is related to symmetry of crystal. If crystal has certain symmetry ...
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1answer
100 views

What would happen to a diamond if it was exposed to near vacuum at room temperature?

I know that coal (graphite) turns into diamond when a high enough pressure is applied, but I guessed it would stay as a diamond unless it was incinerated by a high enough temperature. However, I ...
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1answer
64 views

Why does the rate of melting of an ice block vary in different methods?

I saw that an ice block melts faster when it is placed in a microwave rather than when it is exposed to flame. Could it be because the flame creates a layer of water vapor between the flame and ice? ...
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1answer
128 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
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57 views

Regelation, ice cutting, and snowballs

Pressure decreases the melting point of ice, and applying pressure then releasing it will allow ice blocks to weld together by melting them and letting them freeze. See this video. The detractors of ...
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1answer
23 views

Bose-Einstein phase transition and average number of part in state l

The explanation I have trouble understanding is this: The average number of particles $<n_l>$ on state $l$ is $$<n_l>=\frac{z}{e^{\beta \epsilon_l}-z}$$ where $z=e^{\beta \mu '}$ is the ...
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0answers
51 views

isochoric first-order transition

I wonder how can we classify a phase transition that occurs (at constant volume) without any discontinuity in pressure but with a step in energy? Is it still a first order transition?
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1answer
56 views

How to quantify translational symmetry?

I'm trying to study phase transitions and I'm trying to find a way to classify regions of space based on their "crystallinity". I'm working with 3D coordinates, but I'll present the problem in 2D ...
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0answers
19 views

Vortex-domain wall co-excitation

Both vortices (or disclinations) and domain walls are possible topological defects in a spin system with frustration, but I did't find reference about the interaction of these two. Do any stackers ...
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1answer
47 views

NVT simulation of the phase transition

Why it is assumed to be incorrect to simulate,say, liquid-solid transition at constant volume (NVT simulation)?
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46 views

Is any phase associated with some fixed point in Renormalization Group?

In Wilson's paper I found a lot of discussion in expansions near a fixed point. He suggested that each fixed point is associated with a regime of the system. Like the fixed points of Anderson's Model, ...
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0answers
61 views

What is the physical mechanism of the topological phase transition driven by temperature?

The topological property of topological insulators (TIs) is characterized by the non-trivial topological invariants of their band structures, such as $Z_{2}$ topological invariants. While it's clearly ...
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0answers
55 views

Example of critical (non-relativistic) quantum field theory in 1D?

Is there an example of a critical non-relativistic bosonic quantum field theory in 1D (no time)? So, the field theory can be describe by annihilation, $\psi(x)$, and creation operators, ...
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1answer
178 views

How does the notion of topological order relate to the Landau-Ginzburg theory of phase transitions?

As per Landau-Ginzburg (LG) theory, we write down a theory (Hamiltonian) with all possible interactions/operators (in terms of some order parameter) that respects certain symmetries. The ground state ...