Finite-size effects in layered magnetic systems

TL;DR

This paper investigates finite-size effects in layered magnetic systems with coupled Ising spins, analyzing how specific heat, correlation length, and surface critical behavior are affected near phase transitions, using conformal invariance in 2D.

Contribution

It provides a detailed analysis of finite-size effects and surface phase transitions in layered Ising systems, including exact scaling functions derived from conformal invariance in 2D.

Findings

Maxima in specific heat and correlation length occur at different temperatures.

Finite-size scaling and surface critical exponents are characterized.

Exact scaling functions for order parameter profiles are proposed in 2D.

Abstract

Thermal and magnetic effects in a system consisting of thin layers of coupled Ising spins with $S=1/2$ and $S=1$ are considered. The specific heat and the correlation length display maxima at two different temperatures. It is discussed in what sense these maxima can be interpreted as a finite-size rounding of a thermodynamic singularity associated with a phase transition. The connection with ordinary, extraordinary and special surface phase transitions is made. In $2D$, the surface critical exponents are calculated from conformal invariance. The bulk and surface finite-size scaling of the order parameter profiles at the transition points is discussed. In $2D$, an exact scaling function for the profiles is suggested through conformal invariance arguments for the (extra)ordinary transition.