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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Reconciling the definition and description of SSB in statistical mechanics

In any field theory, Spontaneous Symmetry Breaking (SSB) is defined as a phenomenon where the vacuum state (obtained by minimizing the potential) of the theory does not enjoy the full symmetry of the ...
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Does vapor latent heat depend on temperature? [duplicate]

Adding energy to water makes it's temperature increase. This continues until it reaches 100 °C (at 1 atm) when it turns to vapor with a vaporization energy of 2257 kJ/kg. But if we lower the pressure ...
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Is it possible to estimate the composition of a mixture between ice and liquid water from a temperature heat graph? [closed]

I'm confused whether the equation for thermal equilibrium can be used to obtain the composition of a mixture with only having as information a graph. This happened when I attempted to solve a problem ...
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Asymptotic freedom both in IR and UV

I am wondering if there are any (insightful) examples for models which exhibit asymptotic freedom both in the UV and the IR. I know it sounds odd, but if anyone has come across something like that, ...
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Yang-Lee article on phase transition (1952): possible problem in lemma demonstration

I'm studying the first article of Yang-Lee on phase transition C.N.Yang and T.D.Lee, Physical Review, ”Statistical Theory of Equations of State and Phase Transitions. I. Theory of ...
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Is there a way to perform Ising model simulations with a Game of Life approach?

This question may turn out to be trivial or nonsensical as I do not have more than undergraduate understanding of both the Ising model and computational physics simulations. I just wanted to post ...
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55 views

Definition of glass transition

I am getting confused about the definition of a "glass transition". I read for example that it can be a transition from a rubber state to a brittle state in polymers. In this case therefore I would ...
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What are first and second order phase changes?

In my thermodynamics lecture course, the Ehrenfest equation for a second order phase transition was derived from considering the following graphs, however there was little context in the section for ...
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Order parameter to quantify clustering?

I have a 1D system containing $N$ particles having positions $\{x_1(t),x_2(t),\dots,x_N(t)\}$ in a box of size $L$ with periodic boundaries. The number of particles is conserved. The dynamics of the ...
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Why can you find running water lower than $0^\circ \text{C}$?

I was looking at the phase diagram for water: It seems there is not much of a region on the diagram at which you can be in the liquid phase, for temperatures lower than $0^\circ \text{C}$. I am ...
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Higgs mechanism and phase transition

Generally speaking, phase transitions divide into two types: First order and second order. To me, Higgs field's SSB sounds like a second-order one though I don't know the dependency of Higgs field's ...
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Adiabatic compression of liquid water and vapor in equilibrium [closed]

I'm trying to solve Exercise 6.16 in Garrod's Statistical Mechanics and Thermodynamics. Here is what I've noticed so far. Since $V=n_lV_l+n_gV_g$ where $n_{(\cdot)}, V_{(\cdot)}$ are molar ...
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Can the centre of a rocky planet ever freeze?

When a rocky planet like the Earth or Mars forms the gravitational potential energy is converted to heat energy within the planet. Planets lose heat energy over time by emitting radiation. But is ...
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Does $T \frac{d}{dT} (\frac{L}{T})=C_p(B) - C_p(A)$ hold, where L(T) is the latent heat of phase transition $A\rightarrow B$?

In Garrod's Statistical Mechanics and Thermodynamics, Exercise 6.15 contains the claim that $T \frac{d}{dT} (\frac{L}{T})=C_p(B) - C_p(A)$. But it seems to me that this is false, for the derivative ...
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Phase transition on magnetic materials

Is ferromagnetic to paramagnetic phase transition a reversible process? If I start with a ferromagnetic material with a spontaneous magnetization below the Curie temperature, and then I start to heat ...
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Phase Fluctuations in a BKT transition

The 1D Bose-Hubbard model exhibits a BKT-type quantum phase transition along trajectories of constant density in the $\mu$ vs. $t$ phase diagram (where $\mu$ is the chemical potential and $t$ is the ...
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Ice Melting Faster in Running Water?

Is it me or have anybody else noticed that ice melts way faster in running water than if you keep it in water or just keep it on any rigid surface.The difference is enormous .Why is it so?
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How to define order parameter for a phase which is not polar and not nematic

I am wondering if there is an order parameter that can describe the below phase. It is neither polar and nor nematic. I know that polar and nematic phases can be described by polarization vector $p=...
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Because things smell, is everything evaporating?

Everything, in theory, can have a smell, but that is not the whole point of this question. My main query is, since things do smell, does that mean that everything is slowly evaporating (or, ...
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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/pdf/1808.08635.pdf https://arxiv.org/pdf/1406.1193.pdf https://www.pnas.org/content/pnas/...
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What was above and below the QCD chiral symmetry breaking temperature?

Above a critical temperature in the Universe, there was probably a phase of unbroken approximate QCD chiral symmetry. Mathematically, the symmetry breaking is triggered when the operators $\bar{\psi}{\...
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Some Questions about the Critical Point

I'm currently trying to understand the physics of phase transitions and I'm having a hard time doing that. First of all, the discussions on the topic seem to be confusing and there is no methodical ...
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Is Bose-Einstein condensation a quantum phase transition?

Classical phase transitions are driven by thermal fluctuations which die out at $T = 0$, hence classical phase transitions don't happen at zero temperature. Quantum phase transitions are driven by ...
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Boiling water quites down [duplicate]

When I heat water in my electric kettle the noisy turbulence gets louder and louder as the water nears boiling. Shortly before the kettle turns itself off (presumably when it detects the temperature ...
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Research: Mott insulator and topological order

I'm an experimentalist who is mainly focusing on strongly correlated electron systems (SCES), in particular Metal-insulator (Mott) transitions in the classical example $V_2 O_3$. Recently I decided to ...
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Does stripping electrons from atoms or adding them affect the state of matter in any way?

Does electric charge affect melting, boiling point or sublimation temperature?
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Fixed points in triangular lattice 2d Ising model

Given the following recursion relations: $$K^\prime = 2K \Big(\frac{e^{3K}+e^{-K}}{e^{3K}+3e^{-K}}\Big)^2$$ and $$h^\prime = 3h\Big(\frac{e^{3K}+e^{-K}}{e^{3K}+3e^{-K}}\Big),$$ where $K = J/k_B ...
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Anomalous dimension for 1D quantum Ising model

I am reading Chapter 10.2, Quantum Phase Transition--Subir Sachdev(P144), it said All previous scaling dimensions of the d = 1 Ising model coincided with their so-called engineering dimension; the ...
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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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Surface tension and definition of boiling point

The boiling point of a substance is defined as the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor. Does the pressure ...
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Two particle Heisenberg model with field

I'm having trouble solving a problem with a phase transition of this system. We are considering the following Hamiltonian: $$H=-J \vec{S_1}\vec{S_2}-\mu b (S_{1z}+S_{2z})$$ And I've studied it in ...
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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=...