Crossover Phenomena near Phase Transitions.

Eberhard K. Riedel

A theory for tricritical phenomena proposed by Wegner and the author is described on an elementary level. The emphasis of the discussion is on (i) the differences between critical and tricritical phase transitions, (ii) the crossover phenomena that occur near tricritical points, and (iii) the determination of tricritical exponents, scaling fields and scaling functions. The results have been obtained by renormalization‐group techniques and a scaling field approach to crossover phenomena. The elements of these techniques are briefly explained.

David A. Lavis, Roman Frigg

John F. Nagle

L. De Cesare, L. Craco, Ileana Rabuffo +1 more

A method of investigation of dimensional crossover phenomena in the theory of phase transitions is illustrated for the nite{size crossover.The dimensional crossover phenomena in systems with quenched extended impurities and inhomogeneities as well as the classical{to{quantum crossover at extremely low temperatures are also discussed.The fundamental interrelationship between the effective dimensionality and the ratio of the relevant characteristic lengths of the system is established and applied to the description of dimensional crossover phenomena.

Stephen Powell

Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge theory becomes confining, provide examples of unconventional criticality. This Letter studies the behavior at nonzero monopole density near such transitions, using scaling theory to arrive at universal expressions for the crossover phenomena. For a particular transition in spin ice, quantitative predictions are made by mapping to the XY model and confirmed using Monte Carlo simulations.