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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Why is the Mermin-Wanger theorem not considered for superconductors in 2D?

Several papers set up a model of fermions in 2D and calculate superconducting $T_c$, e.g.: https://arxiv.org/abs/1808.08635 https://arxiv.org/abs/1406.1193 https://doi.org/10.1073/pnas.1620651114 ...
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Why do ice cubes shrink in the freezer?

OK before you all yell "EVAPORATION", I know that's the boilerplate answer, but why and how. Back in high school we were taught water, and most other elements and compounds, have three states, solid, ...
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Landau Theory of Phase Transitions

As often stated in books, near a phase transition we may express the free energy density as a power series in the order parameter $\phi(\mathbf{r})$. Up to quartic contributions, we have $$f=f_{0}-h\...
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Flory-Huggins ternary phase diagram with a neutral component

I am searching the literature for the Flory-Huggins phase diagram with the following components : polymer, solvent, and a third component that does not interact with the other components (just entropy ...
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Do all the classical critical lattice models have emergent conformal invariance?

I understand that any quantum lattice model at the critical point which can be described by a massless relativistic quantum field theory has emergent conformal invariance. My question is what about ...
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Magnetization in Quantum Transverse Ising Model: Mean Field Theory vs Reality

One of the canonical examples of mean field theory concerns the ground state ($T=0$) of the transverse field Ising model, with Hamiltonian $$H = -J\sum_{<ij>} \sigma^z_i \sigma^z_j-h \sum_i\...
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Is there a temperature-pressure phase diagram of carbon dioxide for the lowest temperatures and pressures?

The image above will probably be well known to visitors of Wikipedia on CO$_2$. But is there a temperature-pressure phase diagram of CO$_2$ for still lower temperatures and lower pressures as well ?...
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Which one is colder? Zero temperature ice or zero temperature water?

I like to understand that which one of the following items seems colder, when we touch them? zero temperature ice zero temperature water Why?
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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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Why is there vapour when I take a hot shower?

When we take a hot shower it is pretty common to see a white vapour around the bathroom. But the water I am using is below 100º C. I know the boiling point of the water can be lower than this with a ...
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Why does pressure remain constant during a phase change

Consider the following graph describing a phase change from a liquid state (blue area) to a gaseous state (light blue area). Why does the pressure remain constant in the coexistence area (grey area)?...
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Electric Field Change Freezing Temperature of Water?

I assume that the reason water freezes is because as you decrease the temperature, the kinetic energy of the water molecules decreases and the dipole bonding potential eventually over comes the escape ...
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How close to the critical point is sufficient close for measuring critical exponents?

I am learning Monte Carlo and just manage to simulate a phase transition by computing the heat capacity or the susceptibility. I wish I can also compute critical exponents.To this purpose, I have read ...
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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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Symmetry breaking in Bose-Hubbard model

According to Landau's symmetry breaking theory, there is a symmetry breaking when phase transition occurs. What is the symmetry breaking of superfluid-Mott insulator transition in Bose-Hubbard model?...
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Phase diagram for oxygen

Do you know where can I find simple diagram (solid, liquid, gas) for for oxygen? EDIT: I made a mistake. I wanted oxygen instead of water. sorry.
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Ginzburg Criterion - why average over the Correlation Length?

To derive the Ginzburg criterion for the upper-critical dimension the fluctuations are averaged over a volume set by the correlation length. Why is this done? i.e. why do we average over a volume in ...
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What's the most stable crystal lattice for a collection of spherical toy magnets?

I recently found a bunch of tiny spherical toy magnets, and I've been having fun sticking them into various shapes. In two dimensions, there are only two possible packings of the magnets: a square ...
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Order of phase transitions

I got to read things like In case of a first order phase transition, the volume and temperature change in a discontinuous manner. However for phase transitions of higher order the change in ...
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Does salt affect the boiling time of water?

If I have 1 cup of water on the stove and another cup of water with a teaspoon of salt. would the salt change the boiling time of the water?
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Is Landau free energy really the free energy?

I recall reading in Negele&Orland's book that Landau free energy function is not really the free energy that one obtains from the partition function $$F = -\frac{1}{\beta}\log Z.$$ Indeed, the ...
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What happens to water level when ice XII melts?

There exists this famous idea that if all floating icebergs melt, water level will stay the same (because the water replaced by ice is the volume of the melted ice). Now, Is this always so, if you ...
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What actually makes boiling happen?

Boiling can be breezed over easily with a few rudimentary diagrams and a couple equations, but I seek a deeper explanation. The definition of boiling is that the vapor pressure in the liquid is ...
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The thermodynamics of heating water in a rigid container

When the pressure on the liquid surface is less than the vapor pressure of the liquid at a given temperature, the liquid will start to evaporate. This is common sense. The problem is more difficult ...
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Phase transition in 2D Heisenberg model

When we study the two-dimensional isotropic Heisenberg Model using Mean Field Theory or by Monte Carlo simulation we observe a phase transition at a temperature not equal to zero. This is opposed to ...
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Cosmic bubble collision

I'm reading this review right now. The claim seems to be that when you have an expanding "false vacuum", finite size bubbles form due to phase transition (cause by finite action instantons) (which, in ...
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Why should the vapor pressure exist at all tempratures?

According to P-T phase diagram, at a constant pressure, liquid and gas attain equilibrium only at a certain temperature, (i.e. boiling point). So in a situation where I'm keeping a liquid in a closed ...
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Temperature dependence of the Higgs VEV

Presumably, The Higgs field vacuum expectation value has a strong temperature dependence close to the electroweak symmetry breaking phase transition. Does this have known consequences for the ...
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Derivation of the Poynting and Kelvin equation (Effect of external pressure on vapor pressure)

Consider a condensible liquid. Using the Clausius-Clapeyron equation one can derive an expression for the vapor pressure $p_{sat}$. This is the pressure at which liquid condensat and vapor coexist. In ...
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Phase transition in 3+1 abelian theory

In historical paper A View From the Island, A. M. Polyakov wrote at 6th page: In the abelian case, these dislocations turned to be just the world lines of magnetic monopoles and I predicted the ...
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What kind of phases nanoparticles have (gas-solid-liquid)?

If a phase transition requires a number of particles that is in the TD-limit, can nanoparticles (~10 atoms) have phase transitions? What kind of phases and transitions nanoparticles have?
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Symmetry breaking - mixed state in $T\rightarrow 0$ limit

In the quantum$^1$ system with a continuous symmetry (in the Thermodynamic limit) relating the ground states $\newcommand{\ket}[1]{\left|#1\right>}\{\ket{\theta}\} \newcommand{\bra}[1]{\left<#1\...
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Salt and boiling speed

When we add a compound (salt) to a solvent, the boiling points rises. But, what could we say about the speed the solvent reaches the boiling point? It's better to add salt before or after boiling ...
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How to convert these from the given free energy $G$ vs $X$ to $T$ vs $X$ diagrams?

What I really do not understand is how they are converting from G vs X curves to T vs X. I have a couple of more diagrams with which I am having problems. A detailed answer to this is most welcome.
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How to obtain a nonzero order parameter for a symmetry-breaking quantum phase transition?

If $\hat{m_z}=\frac{1}{N}\sum_i \hat{\sigma^z_i}$ is an order parameter for finite quantum system (transverse Ising model, say), then it will never break the $\mathbb{Z}_2$ symmetry since $\langle\...
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Critical slowing down in Monte-Carlo algorithm for classical 2D Ising Model

Why do local updates (i.e. local spin flips) near the phase transition in MC algorithm for classical 2D Ising model are said to be not "effective" and lead to incorrect critical indices? I understand ...
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Why does the stiffness of organic polymers (plastic) change so much with small changes in temperature?

This is on the borderline between Physics and Chemistry, but I would like a Physics perspective. I am guessing that plastics are a glass-like phase, rather than a true solid.
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Water solidifies near the bottom of a hypothetically deep oceanic trench

How deep (kilometers) would an oceanic trench on planet Earth have to be in order for the water to become a solid because of the pressure from the water column? For simplicity, maybe assume chemically ...
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A query on the equation $TdS = dU + PdV$ (relating to phase changes)

$TdS=dU+PdV$ is one of my favourite equations in all of physics. I have used it many times, in particular to obtain the Helmholtz free energy; my favourite state function. One thing I am not 100% ...
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Do solids do something analogous to liquids evaporating below their boiling point?

I'm probably not entirely right, but evaporation differs from boiling in that it is surface rather than bulk phenomenon driven by a pressure gradient rather than temperature. If a volume of liquid is ...
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Why are seemingly stable parts (i.e., with $(\partial P/\partial V)_T<0$) of the Van der Waals' isotherms also excluded?

Certain unphysical region of the isotherms obtained from of the Van der Waal's equation of state must be excluded because, in this region, volume increases with increasing pressure (i.e. $(\partial P/\...
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Interactions between "particles" to prevent diffusion and to cause phase segregation

The free energy of particles reads, if we assume no internal energy : $\tilde f(c)= \frac{f(c)}{k_bT}=-c \, ln(c)-(1-c)\, ln(1-c)$, with $c$ the concentration. If we had a term $F(c)$ for the ...

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