The Vicinity of the Critical Point

Abstract

Up to now, we have concentrated on describing the results of conformal invariance for the universal finite-size scaling functions Y and S _i of the singular free energy density and the correlation lengths

$$ \begin{array}{*{20}c} {f^{\sin } = L^{ - 2} Y\left( {C_1 tL^{{1 \mathord{\left/ {\vphantom {1 \nu }} \right. \kern-\nulldelimiterspace} \nu }} ,C_2 hL^{{{\left( {\beta + \gamma } \right)} \mathord{\left/ {\vphantom {{\left( {\beta + \gamma } \right)} \nu }} \right. \kern-\nulldelimiterspace} \nu }} } \right)} \\ {\xi _i^{ - 1} = L^{ - 1} S_i \left( {C_1 tL^{{1 \mathord{\left/ {\vphantom {1 \nu }} \right. \kern-\nulldelimiterspace} \nu }} ,C_2 hL^{{{\left( {\beta + \gamma } \right)} \mathord{\left/ {\vphantom {{\left( {\beta + \gamma } \right)} \nu }} \right. \kern-\nulldelimiterspace} \nu }} } \right)} \\ \end{array} $$

(1)

for the case of small values of the finite-size scaling variables z = tL^1/v and μ = hL^(β+γ)/v. We now ask the converse question on their behaviour for z, μ becoming large.