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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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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 ...
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Solid to Solid Vs Liquid to Solid Phase Transition [duplicate]

If we want to achieve Solid phase transition(means a solid transfer to another solid) and Liquid phase transition(means transformation of liquid into solid like water turned into ice..) then which one ...
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Why do we heat salt water to desalinate it rather than freeze it?

Most sea water desalination plants rely on the basic principle of heating water to evaporate it, after which the salt-free vapor is condensed. According to Wikipedia, over half the cost of ...
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What will happen if my room is half filled with dry ice? [closed]

Suppose we have a sealed room, the room is a cube, half the room is filled with dry ice. What will happen when the dry ice sublimates to CO2, will the pressure of the room increase dangerously as the ...
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What is the BKT transition in non-equilibrium systems?

There is a useful page on the BKT (or KT) transition here which describes the role of vortices in 2d equilibrium systems. I am interested in what happens in 2d non-equilibrium driven-dissipative ...
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Relation between phase transitions and free energy?

I'm a mathematics undergraduate student, and I'm struggling with the concept of phase transition. I know that a (quite general) definition of phase transition is that "a physical system undergoes a ...
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Critical points of vector field with zeros in the magnitude

I am studying a vector field which has critical points (sources, sinks, saddle points and centers). The magnitude of the vector field goes to zero smoothly in these points, however. Contrast that to ...
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Phase diagram of a fluid

How is it look like the phase diagram of a fluid in density-pressure plane? I came across the phase diagram in Pressure-temperature plane most of the time. But I can't find the phase diagram in ...
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What is Landau theory, and why is it only valid within a region close to the transition temperature?

I'm aware of the fact that first order and second order phase transitions are distinguished by at what order their free energy suffers a discontinuity as a function of a state variable, and I know ...
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Applying the Clausius-Clapeyron relation

An example of the Clausius-Clapeyron equation, according to Wikipedia, is: I'm a bit confused with the process. As far as I'm concerned, this slope is the rate of change of pressure with respect to ...
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Phase decomposition domain growth Cahn-Hilliard

Is there a way to show analytically or with dimensional analysis that the growth of the domains in phase decomposition and for the long time behavior is 1/3 for Cahn-Hilliard equation ? $\lambda\sim ...
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Real world applications of triple point?

What are the real world applications of triple of water? And is it worth researching what factors could effect it?
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What’s the topology of critical region?

Duhem said the aim of physics is natural classification. I think topology and geometry are a wonderful way to link analogous parts among different phenomena. Thus we can classify and predict facts. ...
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Molecular dynamics: metal clusters

I'm working in molecular dynamics with transition metal clusters. The aim is find the melting point, so, it's necessary scale the velocities to increment temperature. I know that I should use ...
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Landau free energy expansion

On Huang page 417 he talks about Landau Theory and he says that in the neighborhood of a critical point where m(x) is small, we can expand the landau free energy $$\psi=\psi(m(x),H(x))$$ In powers ...
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Cooling effect caused by evaporation

Evaporation is said to cause cooling effect because it absorbs energy from surroundings to change its phase from that of a liquid to gas. I am in doubt as to why would the surroundings be ready to ...
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How to interpret phase diagrams?

I find quite difficult to interpret phase diagrams in general, for example I see people discuss them along the following lines: Here we see the coexistence line between liquid-solid phases.. a ...
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1answer
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Why 2nd-order derivatives of $G$ are discontinuous in 2nd-order phase transition?

In most undergraduate books, it is said that for second order phase transition Gibbs free energy and its first order derivatives are continuous at transition temperature. But the second order ...
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How does ice melt when immersed in water?

When an ice cube is immersed in water at a room temperature, how is the thermal energy from the water transferred to the ice cube? Currently I have two answers: Infrared radiation from the water ...
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What determines the specific value of the order parameter in spontaneous symmetry breaking?

Three examples in the spontaneous symmetry breaking that occurs at a phase transitions: A ferromagnet below the Curie temperature chooses an axis of quantisation along which all the spins align, ...
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Understanding the Clausius-Clapeyron equation

I am confused about what the Clausius-Clapeyron equation is saying basically. I learned it from Finn's Thermal Physics textbook. Here is the illustration they used to derive it. Matter of two ...
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Integrability of a non-integrable quantum spin model at critical point

Is it right, that non-integrable quantum spin models in one dimension become integrable at their critical points? Or do they stay nonintegrable at the critical point also? Are there any examples known?...
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How to know if a liquid is boiling?

Unless we know the boiling temperature of a liquid, how can we know when a liquid is boiling ( I have this doubt because at temperatures nearing boiling point evaporation and boiling cannot be ...
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Absence of phase transitions in quantum 1D systems at positive temperature

While it is generally said that there are no phase transitions in classical lattice systems in one spatial dimension, there are also exceptions to this rule. Rigorous proofs involve some fairly strong ...
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Superconducting order parameter seems to depend on the choice of the ground state wave function!

As it is described in this question the BCS wave function has definite phase but indefinite electron number. Therefore the superconducting order parameter $\langle \phi| c_{k \uparrow}c_{-k \downarrow}...
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Why isn't superconductivity destroyed by the Goldstone modes?

In BCS theory they break particle number conservation and show the existence of a gap, which would explain why groundstate properties stay relatively the same even for higher temperatures (until beta ...
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Basics of topological order and its relation to entanglement

What is a topological order that drives a topological phase transition? How is it different from say magnetic ordering or the superfluid ordering? What is its relation with entanglement? Please ...
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Is it possible to find dry ice crystals lying around the base in Antarctica?

Dry ice sublimates at -78.5°C, while the lowest temperature registered is about -89.2°C around the Vostok station in Antarctica. Imagine a person living on that station on that day (or night, since it ...
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The influence of a temperature gradient on the growth of dendrites in a solid liquid interface

Not sure if this is the correct place to ask... My book states that, for a Solid Liquid interface in which the liquid has an increasing positive temperature gradient (increasing temperatures in ...
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Why are wet bulb temperatures so warm compared to a naive calculation?

Wikipedia defines wet bulb temperature as: the temperature of a parcel of air cooled to saturation (100% relative humidity) by the evaporation of water into it, with the latent heat supplied by ...
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Do Maxwell relations hold during a phase transition?

Maxwell relations are found by taking mixed derivatives of a thermodynamic potential. Does this mean that they do not hold at a first-order phase transition, where the thermodynamic potential is ...
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Phase change in oceans

When ice cube melts in water the level of water doesn't change but when glaciers melts in oceans sea water level increases why?
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Why the correlation function of 2D classical XY model is written so?

2D classical XY model $$H = -J\cos(\theta_{i}-\theta_{j})%$$ is famous for Berezinskii-Kosterlitz-Thouless phase transition. This is because of the difference of correlation function between hot and ...
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Do quantum effects play a role in the evaporation of water?

Imagine a thermodynamic system composed of a tumbler half-full of pure water, composed entirely of 1H and 16O. The system is isolated from extraneous influences by a perfect box impermeable to ...
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Pinch points in fidelity per site (quantum phase transitions)

In Sachdev's Quantum Phase Transitions he defines a quantum phase transition in an infinite lattice as the point in which the ground energy as a function of the parameters of the system becomes non-...
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Why does placing liquid nitrogen in a low pressure chamber lower its temperature?

As you can see in this demonstration and read in this Wikipedia article if you were to place a cup of liquid nitrogen in a low pressure environment then it would reach a triple point and begin to ...
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Vacuum energy in continuous phase transitions

In a first-order cosmological phase transition, the tunneling from the false to the true vacuum (see left picture below) releases false vacuum energy corresponding to the potential difference $\Delta ...
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What are phase transiton in different contexts?

I have come across the concept of phase transitions in various contexts. From simple phase transition between different states of matter like water to ice and so on, to phase transition in magnetic ...
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How do I relate phase shift to heat capacity or thermal conductivity for frequency domain thermoreflectance?

I'm trying to measure either thermal conductivity or heat capacity of Silicon devices using frequency domain thermoreflectance (FDTR). I can get phase shift between the incoming signal from pump laser ...