Self-dual cluster renormalisation-group approach for the square lattice Ising model: specific heat and magnetisation

Abstract

A simple renormalisation-group approach based on self-dual clusters is proposed for the two-dimensional nearest-neighbour spin-¹/₂ Ising model on the square lattice; it reproduces the exact critical point. The authors calculate the internal energy and the specific heat for vanishing external magnetic field, spontaneous magnetisation and the thermal (y_T) and magnetic (y_H) critical exponents. The results obtained from the first four smallest cluster sizes strongly suggest the convergence towards the exact values when the cluster size increases. Even for the smallest cluster, where the calculation is very simple, the results are quite accurate, particularly in the neighbourhood of the critical point.