Dimensional Crossover and Finite Size Scaling Below T_c

Freire, F. and O'Connor, Denjoe and Stephens, C. R. (1992) Dimensional Crossover and Finite Size Scaling Below T_c. (Preprint)

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Abstract

Using the formalism developed in [1] dimensional crossover in an Ising type system below T_c(L) is considered, T_c(L) being the critical temperature of the finite size system. The crossover considered is that on a d dimensional layered system satisfying periodic boundary conditions and of size L. Effective critical exponents δ_eff and β_eff are introduced and shown to crossover between their d and d -1 dimensional values for ξ→∞ in the limits L/ξ_L→∞ and L/ξ_L→0 respectively, ξ_L being the correlation length in the layers. The effective exponents are shown to satisfy natural generalizations of the standard scaling laws. L dependent, global, non-linear scaling fields which span the entire crossover are defined and a scaling form of the equation of state in terms of them derived from an L dependent renormalization group equation. A universal crossover equation of state and effective exponents are obtained to one loop and shown in the above asymptotic limits to reduce to known results.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:13
Last Modified: 19 Jul 2018 10:40
URI: http://dair.dias.ie/id/eprint/741

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