A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion

Abstract

We study numerically the magnetic susceptibility of the hierarchical model with Ising spins ($\sigma =\pm 1$) above the critical temperature and for two values of the epsilon parameter. The integrations are performed exactly, using recursive methods which exploit the symmetries of the model. Lattices with up to $2^{1}8$ sites have been used. Surprisingly, the numerical data can be fitted very well with a simple power law of the form $(1-\beta /{\beta }_c{)}^{-\gamma }$for the {\it whole} temperature range. The numerical values for $\gamma$ agree within a few percent with the values calculated with a high-temperature expansion but show significant discrepancies with the epsilon-expansion. We would appreciate comments about these results.

15 Pages, 12 Figures not included (hard copies available on request), uses phyzzx.tex

References in corpus (1)

• Remarks Concerning Polyakov's Conjecture for the 3D Ising Model and the Hierarchical Approximation

Cited by in corpus (5)

• Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model
• A Guide to Precision Calculations in Dyson's Hierarchical Scalar Field Theory
• The Oscillatory Behavior of the High-Temperature Expansion of Dyson's Hierarchical Model: A Renormalization Group Analysis
• The High-Temperature Expansion of the Hierarchical Ising Model: From Poincaré Symmetry to an Algebraic Algorithm
• A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model