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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How is the temperature constant during evaporation but it has different values depending on the location within the liquid?

During phase change such as water evaporation the temperature is supposed to be constant but it varies within the liquid itself i.e. the highest temperature in heterogenous evaporation is at the ...
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How to prove $(\partial^2 P)/(\partial V \partial T) \leq 0$? (Question about Griffiths’ 1965 Thermodynamic Inequalities and Apparent Contradictions)

I am currently studying a paper by Griffiths (1965b) on thermodynamic inequalities and have encountered some conceptual difficulties with the formulation presented therein. I’m hoping to get some ...
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2d Ising model with a longitudinal field -- do the low and high temperature expansions converge for all nonzero $T$?

The 2d Ising model has a ferromagnetic and a paramagnetic phase separated by a critical $K_c$. The paramagnetic phase is often understood via a high-temperature expansion of the free-energy in powers ...
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Can the edge degeneracy in spin-$2$ AKLT go away on an arbitrarily small $SO(3)$-symmetric bulk perturbation?

I am learning about SPTs, or symmetry-protected-topological phases. There is a rich structure in antiferromagnetic spin chains. The Heisenberg point is gapless in half-integer-spin antiferromagnets ...
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Why doesn't latent heat change the temperature?

Seems like there is this new type of heat in town. Temperature is just the average kinetic energy; heat is basically movement of particles, so basically kinetic energy, so temperature is the measure ...
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How to calculate the specific heat jump for a van der Waals gas at a non-critical volume?

I am currently self-studying Statistical Physics by Professor Schwabl and encountered a problem in the book (problem 5.5) that has significantly challenged my understanding. The problem is brief but ...
John Title's user avatar
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Axion domain wall number and heavy quarks

The domain wall number of a UV complete theory of axion is related to the number of PQ-charged heavy quarks that run in the loop. In the case of KSVZ model, $N_{\rm DW}=1$ while in DFSZ, $N_{\rm DW}&...
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Gas and Vapour liquefaction

I am a bit confuse in the first statement. I think the statement is implying vapour as 'former' and gas as 'latter'. Am I correct here? But gas can be liqufied with pressure alone below the critical ...
Cerebral cortex 's user avatar
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Swap operation in a Radiative Random Unitary Circuit

In ref PhysRevLett.131.220404, the author have studied the scrambling in a Radiative Random Unitary Circuit (RUC) -- a RUC that exchanges qubits with an environment at a rate $p$. It might perhaps be ...
Young Kindaichi's user avatar
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Does having a liquid (less dense than ice) above a floating (in water) ice cube, change the fact that the water level remains constant when ice melts?

An ice cube floats in water, with a liquid (less dense than ice) above it. When the ice cube melts will the water level go up, down or remain constant?
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How do I calculate predicted curves (or surfaces) on a substance's $p$-$T$ (or $p$-$V$-$T$) phase diagram?

I just saw the announcement "Breakthrough in melting point prediction: over 100-year-old physics problem solved by Queen Mary Professor", which says that Professor Trachenko ... ...
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What is a name of a critical point?

Imagine a critical line separating two thermodynamic phases. There is a point on this line splitting the line into two pieces such that on one piece the transition between the two phases is 1st order, ...
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Is there possible isentropic phase transition?

Suppose we have a complex system changing in state but without order parameter jump. Is there possible that during this change particular dynamic of system chsnges enough to name this phase change, ...
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Is RG fixed point always related to a second-order phase transition?

In practice, usually one of the parameters is tuned (for example temperature in 3D Ising model, which is a relevant parameter) so that it coincides with the value of RG fixed point, then RG flow make ...
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Can the temperature of a steel ladle in boiling water exceed the temperature of the water?

I'm debating about this problem with my friends (they and I majored physics. But I think it's not a trivial question.) The problem is : The water in the pot is boiling by the gas stove, and there is ...
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Can latent heat exist when both phases cannot exist at same temperature?

This is my understanding (please tell me if i am going wrong anywhere): During phase change (i.e. ice melting into water) the molecules absorb heat, gain more random kinetic energy, and spread apart (...
Varshil MVH Pets's user avatar
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For a liquid at boiling point, how can it require a set amount of heat (latent heat) to vaporize

I've always had a hard time wrapping my head around the 2 below statements being true for vaporizing a liquid into a gas: When a liquid reaches its boiling point the temperature stops rising (and any ...
LWilkinson's user avatar
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Phase transitions in the XXZ model

Consider the one-dimensional quantum XXZ model defined by the Hamiltonian: $$ H = J \sum_{i} \left (X_i X_{i+1} + Y_i Y_{i+1} + \Delta Z_i Z_{i+1} \right). $$ First, let us focus at zero ...
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What would happen if you add ice to an isolated system of water that is already at 0°C?

So here’s my question: Say there is some ice at -2°C. And water at 0°C. The ice is added to the water. Now this is a completely isolated system. There is no heat exchange whatsoever with the ...
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Yang-Lee circle theorem and the distribution of zeros

I am reading a note on Yang-Lee's zeros. The note first focuses on the grand canonical partition function $\Xi(T, z)$, where $z$ is the complex fugacity conjugate to the number of particles. If the ...
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Why does the freezing point of water regress at select pressures before increasing again at even higher pressures?

This phase diagram of water shows how the phase of water is determined by the pressure and temperature. I find it easy enough to understand; as the pressure increases, the boiling point of water also ...
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Sublattice model for ternary system

Much like in an earlier post of mine, I'm now calculating the phase diagram of a ternary system (Ag-Al-Cu, to be specific), which has some phases modelled as sublattices (using this publication for ...
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Shape of an isochoric curve in T-s and h-s diagrams during phase changes

In the pV diagram an isochoric curve is, of course, a vertical line whereas in the T-s diagram it has the form: $$T(s)=T_0 \space e^{\frac{s-s_0}{c_V}}\tag1$$ so it is an exponential function (steeper ...
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Use of Binder Cumulant for Determining Critical Temperature

I am completing a computational project where I am simulating the Ising model using Monte Carlo methods, namely the Metropolis-Hastings algorithm, and the Wolff algorithm. For the Metropolis-Hastings ...
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How are states of matter determined experimentally?

Let's consider for example water. There is the classical phase diagram shown below which depicts the three states liquid, solid, and gaseous. My question is, how were the exact positions of the ...
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Phase change first then raising temperature, is it possible? [closed]

We have a liquid at $X^{\circ}$ Celsius , we want to convert it to $Y^{\circ}$ Celsius gas 1: $X^{\circ}$ Celsius liquid absorb latent heat of vaporisation, turn into $X^{\circ}$ Celsius gas, and then ...
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The 2d Ising transfer matrix and the effect of anisotropy on more general transfer matrices

The 2d Ising model has a row-to-row transfer matrix that can be written suggestively as $$T = e^{\tau \sum_i \sigma^z_i \sigma^z_{i+1}} e^{ \lambda \tau \sum_i \sigma^x_i}$$ where $\tau$ and $\lambda$ ...
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Intuition for smaller upper critical dimension in quantum statistical physics

In the theory of phase transitions, the upper critical dimension (UCD) is the dimension of space above which the phase transition is well captured by mean-field theory. For instance, it is well known ...
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Ferromagnetic Potts models in a field and the endpoint of their first-order lines

The $q=3$, $d=3$ ferromagnetic Potts model has a first-order transition on varying temperature. I recently learned that at small $h>0$, where $h$ is a field favoring one of the three colors, there ...
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Does there exist a 2d continuous phase transition that is first-order in mean-field theory and satisfies the Harris criterion $\nu>1$?

I am looking for an example of a clean, local $d=2$ classical model that undergoes a continuous phase transition on varying temperature that satisfies two properties: The phase transition is ...
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Criteria for neighbors when calculating 2D lindemann parameter

I am trying to compute 2D lindemann parameter to quantify melting in colloidal crystals from particle coordinates obtained in 2D. The equation I have come across for computing 2D lindemann parameter ...
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Does Andrews curve's density in Liquid- Saturated vapor phase change region vary or not?

Are Andrews Curve (isotherms) for gas-liq phase change less dense for low values temperature and more dense for high value of temperature? I came up with this because of Clausius Clapeyron Equation ...
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Possible divergence of susceptibility without spontaneous symmetry breaking?

In the article Strange Metals as Ersatz Fermi Liquids , the authors mentioned in the left bottom paragraph on page 4 that Furthermore the diverging susceptibility of an order parameter at a quantum ...
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Inverting a bubble interface to recover the level set function

I have access to some high quality CFD data that includes 2D and 3D level set functions for simulations of bubbles. Masking the level set function using a heaviside is easy and it is a fast way to get ...
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Phase co-existence and Gibbs free energy

Accoring to Callen's "Themodynamics and introduction to thermostatistics", second edition, page 157, the principle of minimum Gibbs free energy states: The equilibrium value of any ...
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Example of first-order quantum phase transitions between two gapped phases with unique ground state in local 1d spin chain without extra symmetry

I'm trying to better understand first-order phase transitions in local, 1d quantum systems, particularly spin chains. I realized that I don't have a strong understanding of what's possible and ...
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Understanding the binodal and spinodal curve in phase transitions

Consider the following graph, which shows the Gibbs free energy per particle for a Van der Waals gas (the x axis is volume per particle, $v$ and the y axis is free Gibbs energy $G$): Each curve has ...
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Effect of impurities on boiling and freezing points

When impurities like salt is added to water, the boiling point of water increases because of what I think is vapour pressure, though I know very little about that too. However, with the same analogy, ...
Ayush Singh's user avatar
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Existence of low temperature phase in 2-Dimensional XY-Model

I'm reading the lecture notes of David Tong on Statistical Field Theory, specifically chapter $4.4$ on the Kosterlitz-Thouless Transition. He considers the XY model in $d=2$ dimensions and states the ...
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Why are domain sizes of all lengths when the correlation length is infinite at $T_c$?

Given that the correlation length diverges at the critical point, why are domains of finite size? What is the relationship for a ferromagnet between correlation length and domain size?
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When will vessel start heating when ice inside is heated?

If we have an aluminium vessel containing ice at 0 °C and we supply heat to it. Will the ice first melt completely and then the temperature of the whole system increases or will the vessel's ...
Madhav Mittal's user avatar
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Phase transition in Ising Model

Consider the NN Ising model as \begin{equation} H = -J \sum_{<ij>} \sigma_{i} \sigma_{j} - h \sum_{i} \sigma_{i} \end{equation} This model has a global $\mathbb{Z_{2}}$ symmetry in the absence ...
Santanu Singh's user avatar
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Why and How Moly (Molybdenum) can melt at 800°C inside muffle furnace?

I kept a ceramic cylinder wrapped in a Moly sheet. This whole thing was kept on an another Moly sheet inside muffle furnace. I ramped up the muffle furnace to 800°C in half an hour, kept there for ...
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Why can ice melt below 0°C ?

In our common understanding, ice needs to be above 0°C to melt. I have now done an experiment: a piece of glass covered with ice on one side and a heating module on the other end. Placing it in a -20°...
Smith Alice's user avatar
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What's the percentage/relationship of evaporative cooling applied to the liquid by an evaporating/expanding gas?

The example below is simply to provide illustration of the problem. This isn't a homework question. I'm trying to visualize the relationship between liquid and gas at the boundary and I'd appreciate ...
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In physics, when should one use and not use calculus?

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface ...
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Why non-extensive terms cancel out in the low temperature expansion of 2d Ising model?

I'm currently reading David Tong's lecture on Statistical Physics, and I cannot understand the logic in the following paragraph about the low temperature expansion of 2d Ising model. It can be ...
Jason Chen's user avatar
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Why does a mixture of bulk $\rm Hg$ + $\rm Cd$ +$\rm Te$ melt at a much lower melting point than any of its constituents?

In a real life setup, a mixture of $\rm Hg$, $\rm Cd$, and $\rm Te$ melts at approximately 330 degrees Celsius. The element with the lowest melting point is Te which melts at 449.5 degrees Celsius. ...
Terence Fisher's user avatar
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Refrigerated vacuum Soxhlet extraction

Say one wanted to efficiently extract a temperature sensitive and easily oxidized compound from a substance. I envision a Soxhlet apparatus filled with a very low BP solvent like diethyl ether. Rather ...
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Free energy as a function of temperature over phase transition in molecular dynamics simulation

I've constructed a low density standard MD simulation (in Python), using the Lennard-Jones potential with an Andersen thermostat, of 10 particles in a box V = 10 $\times$ 10 $ \times$ 10 in the NVT ...
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