Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques

Jean-Yves Fortin (1) , Maxime Clusel (2)

1 LPTH - Laboratoire de Physique Théorique
2 CSMR - Center for Soft Matter Research [New-York]

We propose a method to study the second-order critical lines of classical spin-$S$ Ising models on two-dimensional lattices in a crystal or splitting field, using an exact expression for the bare mass of the underlying field theory. Introducing a set of anticommuting variables to represent the partition function, we derive an exact and compact expression for the bare mass of the model including all local multi-fermions interactions. By extension of the Ising and Blume-Capel models, we extract the free energy singularities in the low momentum limit corresponding to a vanishing bare mass. The loci of these singularities define the critical lines depending on the spin S, in good agreement with previous numerical estimations. This scheme appears to be general enough to be applied in a variety of classical Hamiltonians.

Mots clés: Ising models; Grassmann algebra; critical point

Domaines: Mécanique statistique [cond-mat.stat-mech]

Jean-Yves Fortin, Maxime Clusel. Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2008, 78 (17), pp.172402. ⟨10.1103/PhysRevB.78.172402⟩. ⟨hal-00332391⟩