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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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Metropolis Monte Carlo Phase Transition for small systems

Metropolis Monte Carlo simulation for the argon liquid fails to reproduce correctly the pressure-temperature isotherm from the point of liquid-vapour coexistence: Why such a phenomenon appears ? The ...
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Loschmidt Amplitudes In Tight Binding Models

I am trying to understand the calculation in this paper which experimentally looks at dynamical phase transitions in a driven (shaken) haldene-like model. The definition of the Loschmidt Amplitude is ...
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What happens when the saturation pressure of a substance is greater than its actual pressure

I am facing difficulties with understanding the relationship with saturation pressure and the phase change (from liquid to gas) of a pure substance. Let's suppose I have some amount of water at p = 5 ...
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Confusion on real space renormalization group for Ising model on lattice

For the Ising model with only nearst neighbor interaction on square lattice, if we do the RG by integrating out half degree of freedom, then we would get a new Ising model with many kind of ...
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Phase transitions, external and internal pressure and boiling

Let's say I have an open container of liquid. According to what I have read, to get the liquid to boil, the vapour pressure has to equal the atmospheric pressure (or there about). I can understand ...
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Potential energy surface for a diatomic molecule desorbing from a surface

I have been asked to sketch the potential energy surface as a two-dimensional contour plot as a function of the vertical distance between the center of mass of A2 and the solid S, and the internuclear ...
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How do the fluctuations of the order parameter depends on the dimensionality of the system?

In Landau theory of second order phase transitions, how do the fluctuations of the order parameter depends on the dimensionality of the system? In superconductors, the fluctuations of the order ...
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Phase transtions. Why has Ehrenfest classification been replaced by modern classification?

Why did modern classification replace Ehrenfest classification? What are the advantages of the modern one?
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Mixture with a strange free energy curve

I have the following energy landscape for a binary mixture with a specie $1$ of volume fraction $\phi$ (it is composed for example of colloids) and a specie $2$ of volume fraction $1-\phi$ (for ...
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Overconstrained equilibrium binary mixture phase seggregation

Assume a binary mixture, with the component $A$ in concentration $c$ and the component $B$ in concentration $1-c$. The total energy $E(c)$ is thus given by a function of one variable $c$ (if we do not ...
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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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Calculate an order parameter for a given set of atomic coordinates

I have a box which contains a few thousand atoms, and I would like to be able to calculate a single number which gives some indication of how ordered their arrangement is in 3D. For example, if they ...
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Melting gold at room temperature?

https://www.sciencedaily.com/releases/2018/11/181120125750.htm I'm skeptical about how the researchers claim that the gold melted at room temperature. Isn't what's really happening is that the ...
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C60 Melting Point Data\Understanding Discrepancy

Why is it that the melting point of C60 is tabulated by many sources ([1],[2],[3]) as being in the range of ~500K and that it sublimes ~800K but in a few molecular dynamics papers I've seen including "...
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Aren't nearly all materials Phase Change Materials?

I was reading about use of parrafin in melting snow Linked from https://ceramics.org/ceramic-tech-today/paraffin-offers-superior-solution-to-road-salt-for-melting-snow-ice links to http://www....
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Why are RG flow fixed points associated with different phases?

Why are RG flow fixed points associated with different phases? I thought the RG makes only statements about behavior near to critical points... a definite phase is far away from the critical point, ...
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What is finite size scaling theory?

The question is in the title. I read some articles about it but I could not understand it completely. What does it mean when we say scaling of any system? Can you please give a brief introduction ...
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Why we can not observe phase transition in finite systems? [duplicate]

In condense matter physics books it is mentioned that we can not observe phase transition in finite systems. Why is it so?
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Can Heat Transfer occur between two bodies with the same temperature but different states only through Latent Heat Transfer? [duplicate]

I understand that temperature difference is the driving force for heat transfer but I have been wondering whether there would be any heat transfer, let's say if steam at 100 degree Celsius and water ...
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Boiling water in metal pot

This is something I've observed when boiling water for tea. I place the water in a metal pot and bring it almost to a boil. The water level is at about the middle of the height of the pot. When the ...
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Kibble Zurek Scaling for Topological Phase Transitions

To begin with my understanding of Kibble Zurek scaling is limited to the following : Given we have a phase transition from one phase (P1) to another (P2), the rate of quench is proportional to the ...
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What is the difference between non-equilibrium and equilibrium phase transitions?

My question is about the distinction between certain kinds of phase transitions. I understand what the difference between first and second order ones are. What is the difference between non ...
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Mean field 3d Ising model in Landau theory

I am solving a problem for some course I am following. I am given the Hamiltonian: $$H = 3NJ \langle \sigma\rangle ^2 -6J\langle \sigma\rangle \sum_i\sigma_i,$$ where $i$ sums over all sites ($=N$)....
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What is the topology of a phase diagram?

Looking at various two-variable phase diagrams I was struck by that on every one I have seen so far all the phases formed simple connected regions; see, for example the phase diagrams of $H_2O$ or of $...
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What is direct interaction, if exist, between gluons and pions?

Gluons mediate the strong force between quarks. Pions mediate the nuclear force or nucleon-nucleon interaction or residual strong force. I had thought of some scalar bosons for my idea because if I'm ...
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Potential Energy of Particles

I read the following statement in my textbook While a liquid is boiling, the energy supplied to the liquid goes to breaking the bonds between neighbouring molecules. Can anyone explain the process ...
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Phase transitions and Helmholtz vs Gibbs Free Energy

Gibbs phase rule for Gibbs free energy says that phases during a phase transition must be in mechanical, chemical, and thermal equilibrium, e.g. $T_1=T_2$,$G_1=G_2$, and $P_1=P_2$, where the ...
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Why is it that all metals do not become superconductor by lowering the ambient temperature?

Aluminium becomes a superconductor at a temperature below $1.91$K. But I am quite certain that all metals do not exhibit superconductivity even when the temperature is lowered to nanokelvin or below. ...
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Melting ice inside water by increasing pressure

An ice cube is floating in water inside a container and the system is in thermal equilibrium. And let say we somehow immerse the ice cube slowly into deeper region inside the container (we may pull a ...
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Variation/Differential in Critical Radius of Homogeneous Nucleation

Getting the critical radius during nucleation from G(r) is straightforward - but in our lecture notes, a notation is used that I cannot quite wrap my head around: The molar Gibbs Free Energy $G(r)$ ...
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Ising Model with site-dependent magnetic field

Consider an Ising system in an external field, which is different at different sites. The Hamiltonian of the system is given by $H = -J\sum_{<i,j>}^{}s_i s_j - \sum_{i}^{} h_i s_i$ Here each ...
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How fast could CO$_2$ ice near the south pole of Mars sublimate?

On Space StackExchange i asked this question about sublimating the CO$_2$ deposit near the south pole of Mars. Uncovering a part of the deposit could cause the CO$_2$ ice to sublimate by the ...
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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: "...
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Long Range order in 2D Ising model

We know from the exact solutions for 2D Ising model on square lattice the long range order appears bellow critical temperature, but how does this agree with the Mermin-Wagner theorem, from which we ...
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Phase transition 2D Ising model magnetization around critical temperature

I am stuck on a part in the derivation of the critical exponent of the magnetization in case of the 2D Ising model. I know that I should find $M \propto (T_c-T)^{1/8}$ but I am having some trouble ...
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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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Pressure of a liquid when discussing boiling

It's said that at boiling point the pressure of the liquid is equal to the pressure of its vapor. That way, bubbles can form in the liquid phase. However, unless I'm mistaken, while the pressure of a ...
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If states of matter transition discretely or continuously

When you see phase diagrams for states of matter, they typically look something like this: This shows discrete changes from one state to the next. I am wondering though if it is actually a discrete ...
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Quantum phase transitions in a finite lattice

Sachdev begins his book on Quantum Phase Transitions by asserting that, for a system on a finite lattice, the ground state energy of a Hamiltonian H(g) (where g is some coupling) is a smooth, analytic ...
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What is the broken symmetry in a phase transition into Anderson localisation?

Anderson localisation is a state of matter where there is no diffusion of particles because of randonmness in the potential landscape. The wavefunction is localised, i.e. exponentially dropping to ...
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Dynamic critical exponents of Curie-Weiss model

I'm looking for the dynamical exponent z (relaxation time) of the Curie-Weiss - Ising like model with infinite-range interactions ($J \sim 1/N$). Does anyone know a reference where this was solved? ...
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Why a superconductor expel magnetic lines of force from inside completely when cooled below critical temperature?

Suppose a superconductor which is in a normal state (i.e. $T>Tc$) is subjected to a magnetic field. As soon as magnetic field switched from 0 to some value, eddy currents will develop on the ...
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Phase Transitions from a Bayesian Perspective of Statistical Mechanics

I have been reading papers by E.T. Jaynes recently about viewing all of statistical mechanics as just Bayesian inference applied to physics. (For an introduction: https://journals.aps.org/pr/abstract/...
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Why is boiling a non-equilibrium process? [closed]

Boiling is a non-equilibrium process. Which equilibrium (mechanical, chemical and thermal) are not maintained during boiling and why?
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Classical Heisenberg Model Using Mean Field Approximation

Suppose we have the Classical Heisenberg Model of N spins $\vec S_i$ (unit vectors), external field $\vec H // \hat z $ $$ {\cal{H}} = -2J \sum_{<i,j>} \vec S_i \cdot \vec S_j - gμ_B \sum_i \...
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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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Trouble with critical expotent β

In the context of the Landau Theory of phase transitions, applying the mean field theory in an attempt to describe transitions such as the Nematic - Isotropic, the Landau energy density is given by $...
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Susceptibility in Bifurcations

In dynamical systems a bifurcation describes the phenomenon where, as a system parameter is varies, a qualitative property of the system might be altered. Similarly, in statistical physics, a ...
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How to numerically calculate Fisher zeros?

The main quantity in the study of dynamical quantum phase transition (DQPT) is Loschmidt echo amplitude defined as $G(t)=\langle \Psi_{0}|\Psi_{0}(t)\rangle=\langle \Psi_{0}|e^{-iHt}|\Psi_{0}\rangle$...
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Why does ice form when you break the seal on a very cold bottle of water? [duplicate]

I put a sealed bottle of commercially available drinking water in a freezer and let it get really cold, but not frozen solid. The water is not carbonated. Then I remove the bottle and place it in a ...