Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Articles dans des revues à comité de lecture

Second-order critical lines of spin-S Ising models in a splitting field using Grassmann techniques
Fortin J.-Y., Clusel M.
Physical Review B - Condensed Matter and Materials Physics 78 (2008) 172402
DOI : 10.1103/PhysRevB.78.172402
ArXiv : arxiv:0810.3601 [PDF]

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 multifermion 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.



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