The two-dimensional ±J Ising spin glass: a model at its lower critical dimension

Fernando D. Nobre

Physica A: Statistical Mechanics and its Applications, 2003, vol. 319, issue C, 362-370

Abstract: The ±J Ising spin glass [probabilities p and (1−p) associated with ferromagnetic and antiferromagnetic couplings, respectively] is studied, at zero temperature, on a hierarchical lattice that approaches the square lattice. It is shown that, for a wide range of values of p [between (1−pc) and pc, where pc represents the critical value of p separating the paramagnetic and ferromagnetic phases at zero temperature (pc≅0.89)], the renormalized probability distribution for the coupling constants {Jij} approaches a fixed shape, after a few renormalization steps. An analytical expression for the fixed probability distribution, in terms of six delta-function peaks with a large predominance in the weights associated with the ±J peaks, is proposed. Such a result indicates that the present model is at its lower critical dimension, for the whole range from (1−pc) to pc, characterized by a stiffness exponent y=0.

Keywords: Spin glasses; Renormalization; Lower critical dimension (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:319:y:2003:i:c:p:362-370

DOI: 10.1016/S0378-4371(02)01511-X

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