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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What to use as reference state for free energy curve of a gas?

My goal is to determine the temperature at which xenon would sublimate (if it didn't turn into liquid first). To do this, I set the free energy of solid Xenon equal to the free energy of Xenon gas, $ ...
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How to calculate the correlation length from the (connected or disconnected) correaltion function?

Here, "How to determine correlation length when the correlation function decays as a power law?" has a similar question, and Adam gave a good answer. However, I don't know how to derive the ...
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Magnetization of the Ising model for an asymptotic vanishing magnetic field

I am considering the following ferromagnetic Hamiltonian for the 2-d Ising Model, say with periodic boundary condition in the torus $\Lambda_n=\mathbb{T}^2_n := (\mathbb{Z}/ \mathbb{Z}_n)^2$: $$ H_n(\...
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Does the magnetic exchange constant $J$ change upon entering the ordered state?

It is known within the Ising or Heisenberg model that the exchange constant $J$, combined with the dimensionality and connected-ness of the system, sets the temperature scale for a phase transition ...
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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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Can a phase transition simultaneously be quantum and classical in nature?

A quantum phase transition (QPT) occurs strictly speaking only at $T=0$, at a point where the gap in the Hamiltonian closes. At finite temperature, the transition becomes less sharp and a 'quantum ...
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Confusion about internal energy and temperature during a phase change

During a phase change, internal energy of a system will change because energy must be added or subtracted (depending on "direction" of change) from the system in the form of latent heat. However, the ...
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Function to describe changes in water's phase diagram

I measured the barometric pressure over 4 days and I obtained the next image: The Y axis is the pressure in hPa and the X axis is the time (4 days) I think it is very interesting the fact that the ...
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Liquid to gas transition - not vapour

Is there a name for a direct liquid to gas transition which is not vapour in an intermediate stage? It seems the name 'vapourisation' is not suitable in this circumstance. Yet boiling is usually ...
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1D Ising model thermodynamic limit

The partition function for the infinite range Ising model is $$Z(\beta ,h)=\int_{-\infty}^{\infty}dm \frac{1}{\sqrt{2\pi/N\beta J}} e^{-Ng(m)}$$ where $g(m) = \frac{\beta J}{2}m^2 - \ln\left[2\cosh(\...
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Paradox regarding phase transitions in relativistic systems

The main question I would like to ask is whether quantities such as density are dependent on the frame of reference. I have searched several forums and the answer is somewhat controversial. Some ...
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So what, exactly, is latent heat?

I am given to understand that the energy is stored in the molecule in the form of changes to bond angles. With water, the bond angle between the hydrogen atoms changes by a degree or so during ...
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Latent Heat using thermodynamic arguments

Is there a way to demonstrate using thermodynamics(or statistical mechanics) and the fact that $\frac{\partial G}{\partial P}$ is discontinuous(in thermodynamic limit) or has a very sharp change at ...
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Finite Size effects in phase transition

I was reading Nigel goldenfeld's Lectures on Phase Transition and Renormalisation Group and came across the following statement: 'If there were perfect instrumental resolution, a change in the ...
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How does phase transition occur in finite sized ising model?

I was simulating the square lattice Ising model via Metropolis Algorithm and found that at 0 magnetic field, there is spontaneous magnetisation below some temperature. I have used Periodic Boundary ...
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Heat-bath algorithm of 2D XY model

Can anyone suggest any reference where the heat-bath algorithm for the classical 2D XY model has been discussed in detail. I have found references for the 3D Heisenberg model which can be exactly ...
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What's the equilibrium that results if a solid is placed in an empty container at constant temperature?

I'm confused at how to approach this question (in a chapter on phase transitions) since it is so general. My first instinct is to say that is depends on the materials P-T diagram and the temperature, ...
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Solution Cahn-Hilliard 1d for a domain of finite size

I'm trying to get the solution of the Cahn-Hilliard equation in 1d with a certain mass $C$. We have two components, and let's assume we have the relation $c_1+c_2=1$.Hence we take only the variable $c=...
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Is there a commonly accepted definition of a quantum phase definition for a finite lattice/set of particles?

As noted by Sachev, and in a previous question, https://www.physicsoverflow.org/41602/, there cannot be quantum phase transitions for finite systems (with bounded local Hilbert space dimension). The ...
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Will a metastable solid convert to it's more stable form upon heating to the transition temperature of the more stable form?

Let's say a solid has a stable phase (A) that exists below some temperature, T, and A transitions to another stable phase B above that temperature. If you take a solid sample of B and rapidly quench ...
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phase transitions and hysteresis

Some phase transitions exhibit a jump, while others exhibits hysteresis. I have read that jumps correspond to the Maxwell construction while hysteretic transitions correspond to the "delay convention"...
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Melting ice made with tap water

I recently froze some tap water in plastic bottles and I later made the ice melt completely (the idea was keeping ice bottles nearby me to fight the heat). When the water returned to liquid a lot of ...
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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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Shape of isotherms in $P$-$V$ phase diagram

Please explain the shape of the isotherms in this P-V phase diagram. In particular, why are the isotherms flat in the liquid-vapor region? (image from Lumen Learning | Physics | Phase Changes)
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Flow velocity ambiguity in transition region

I have calculated the following short table concerning the stationary flow of water in a 1 meter long pipe with a diameter of 16 mm and a completely smooth inner surface. The flow is driven by the ...
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Kosterlitz-Thouless transition and renormalisation group theory [closed]

I'm trying to understand the Kosterlitz-Thouless transition in 2d systems. There is a section in Altland and Simons' Condensed Matter Field Theory that discusses the phenomenon, but I don't really ...
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Is the Mpemba effect exclusive to water?

Is the Mpemba effect exclusive to water ? So I was reading this post about really cool phenomena where hot water freezes faster than cold water. But it only talks about water. Even online student ...
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Non-ideal Gases under fixed external parameters

When discussing non-ideal gases, the first qualitative observation that is made is that specifying the internal parameters of a system does not uniquely determine an equilibrium state. The possible ...
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Different concepts of phase transitions in spin models

I am currently revising the lecture notes in which different spin systems are analyzed, focussing on the occurrence (or absence) of phase transitions. Different techniques are applied to analyze the ...
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How are drawing common tangents to get diffusion different for concave and convex phase fields?

Whenever there is a concept of diffusion involved and we need to decipher what is going to happen we tend to draw common tangent s in the phase field diagrams and decide which direction the diffusion ...
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Is energy minimization a valid consideration even in dynamic/evolution based problems like phase transitions?

As an example, binary mixture phase separation in liquid due to quenching is typically explained by saying that because of decrease in temperature, the free energy landscape is such that splitting up ...
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Why doesn't the phase diagram of water look different?

How can sublimation occur at much lower temperatures than 0 degrees celsius provided that the pressure is sufficiently low? The melting point of water is relatively unaffected by the external pressure ...
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How do we cool gases to the $mK$ range?

When we set new records for coldest temperature in the universe, we usually do it with gases (see: https://physicsworld.com/a/millikelvin-cooling-of-large-molecules-is-no-myth/) How do we pull this ...
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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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QM explanation why hot oil explodes when water pours on it [closed]

I have read this question: Why does hot oil explode when pouring water on it? It explains in a classical way clearly, that the boiling point of oil is hotter then water, and water changes to steam ...
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What are the necessary or sufficient conditions for a renormalization group scheme to be “valid”?

Suppose I have a super operator $G$ which acts on Hamiltonians to produce a new Hamiltonian that is related somehow. For the purposes of this question, suppose that these Hamiltonians are defined on ...
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Thermal hysteresis and its physical significance in lipid membranes?

We usually associate the phenomenon of hysteresis with memory in the system. For example, magnetic hysteresis is the basis of hard disks(if I recall it correctly). There are also electronic circuits(...
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Is a single radon-daughter atom in air, such as ${}^{218}\text{Po}$, a solid?

Is a single radon-daughter atom in air a solid? The Wikipedia article on radon says: Unlike the gaseous radon itself, radon daughters are solids and stick to surfaces, such as dust particles in ...
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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 do soft Pomerons become hard?

The exchange of soft Pomerons (and Reggeons) ($\alpha_R(0)=0.55$ and $\alpha_P(0)=1.08$) seem to describe total hadron-hadron cross sections pretty well in the Regge limit. See, for example: https://...
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How can the Higgs field “sense” that the temperature is high enough to restore the broken symmetry above this temperature?

In the picture below of the potential of the Higgs field, we can see that the field has its highest energy if the field is zero, i.e. if no Higgs particles are present. The symmetry is restored at ...
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Does superheated water have the same temperature as boiling water at room pressure?

According to David Tong’s notes on statistical physics on pages 139 to 140, a superheated liquid lies on an isotherm between the spinodial curve and the coexistence curve. Hence, does this mean that ...
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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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Renormalization Group - Scaling fields and physical critical exponents (1D Ising model)

This is related to this question: Critical exponents and scaling dimensions from RG theory. TLDR: How to compute physical critical exponents $\alpha, \beta, \gamma, etc$ from the RG exponents when ...
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Water steam drops after adding ice cubes

Whenever I fill a glass with cold tap water and then add some ice cubes to it, I usually make the following observation: After a few minutes, the glass' outer surface has (what I assume to be) a ...
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Is evaporation a kind of phase transition?

When liquid is heat up to a critical temperature $T_{c}$, it starts boiling and converting to gas. In statistical mechanics, we learn that it is a phase transition. We studied all the properties near ...
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Charge-Vortex Duality for Bosons

Consider a (2+1)d continuum field theory with the Minkowski action $$\mathcal{L}=|\partial\phi|^2-r|\phi|^2-u|\phi|^4,$$ where $\phi$ is a complex field. The theory undergoes a quantum phase ...
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Graph dimension and phase transitions

In this question I am mainly concerned with phase transitions associated with symmetry breaking. For phase transitions of this type, there are a number of results describing the relationship between ...
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Reference request: good introduction to landau theory and phase transition

My background is in statistics, so I am not well versed in the details of physics, lattices, and ideal gases, etc.--beyond my high school familiarity. However, I have been looking at some models of ...