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Current work supported by DMR-1101189


Continuous Transitions

Phase transitions whose first derivatives of the free energy are continuous are referred to as Continuous Transitions. Their thermodynamic properties are determined by a single length scale called the correlation length. This correlation length diverges at the transition temperature.

Correlation Length

The correlation length describes the spatial extent of fluctuations about the average. It is the distance over which deviations from the average of some quantity can be correlated. An example is the density fluctuations in a gas in thermal equilibrium. There could be an area with a slightly higher density then the average, like a droplet of near liquid density in the gas. Although there will be a distribution of droplet sizes, there is a well defined average droplet size. Roughly speaking this average size is the correlation length. A more abstract example is the distance fluctuations in the energy density of liquid helium are correlated.

Critical Phenomena

This refers to the physics associated with a critical point. Typically some intrinsic length in the system diverges as a power-law as the system approaches this point. The region over which this power-law behavior is obeyed is called the "critical region", and the power-law exponents are called "critical exponents". Interestingly, these critical exponents are not necessarily different for different systems that demonstrate critical behavior. This is know as Universality. Systems which are members of the same Universality Class all share the same critical exponents. This allows one to infer behaviour about one system from studies performed on a different system in the same universality class.

Finite-Size Effects

Finite size effects are deviations from the thermodynamic limit, caused by systems having finite sizes. In everyday situations these deviations are to small to observe. However, situations can arise when the dimensions of a system are comparable to length scales associated with thermodynamic responses. In these situations finite size effects become much more apparent.

Proximity Effects

When two separate thermodynamic systems are placed in close contact with each other the responses near the interface are altered. In superfluids and superconductors this has traditionally been explained by the order parameter of one system, a wave function, not terminating at the interface but decaying as it enters the neighboring system. This decay is an exponential decay on the length scale of the correlation length. Recently there have been measurements of proximity effects over much larger distances which cannot be explained with the traditional understanding.


Scaling theories say that under suitable conditions a finite system can be described by scaling functions which depend on only one variable. They predict that all the data from various confinements will collapse onto a universal locus. This locus will depend only on how many dimensions are confined and the universality class of the system being studied.

Superfluid Helium

At 2.1768K liquid Helium undergoes a continuous transition from a normal liquid to a superfluid. The normal liquid behaves much like water or any other liquid you may be familiar with. The superfluid phase behaves much more interestingly. Among its properties are a near zero viscosity and infinite thermal conductivity. The former allows the liquid to flow through the tiniest of cracks, while the later implies that superfluid Helium will not boil. We use Helium in our research for various reasons. It is in the same universality class as two dimensional ferromagnetic systems as well as superconducting systems, both of which are of great interest for industrial applications. Also it is very easy to have extremely pure samples of helium. At the temperatures where helium goes superfluid almost all impurities will be frozen out, this makes it much easier to measure, accurately and reproducibly, quantities throughout the critical region.

Thermodynamic Limit

The Thermodynamic Limit refers to systems where the dimensions of the system are much larger than any length scale associated with thermodynamic responses. In this limit knowledge of the shape of a sample are not relevant. Formally the thermodynamic limit is the limit in which the number of particles N and the volume of the system V become so large they are considered infinite, but the particle density N/V remains finite. Systems in this limit are often referred to as "bulk" systems.

Transition Temperature

This is the temperature at which the system undergoes a phase transition. For liquid helium, this is the transition between normal liquid and superfluid.


Universality refers to the idea that two different systems can share the exact same critical exponents. Systems that share critical exponents are said to be members of the same "Universality Class".

Universality Classes

A universality class is a group of systems that share the same critical exponents. Members of a class have three things in common, Symmetry in their Hamiltonians, dimensionality, and the ranges of forces. Our system, liquid helium near the superfluid transition, is a member of the "XY" universality class along with two dimensional ferromagnetic systems and superconductors.
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Last Updated: Wednesday, 24-Aug-2011 15:52:24 EDT by JKP