Phase diagram of the two-dimensional +/-J Ising spin glass.
The +/-J Ising spin glass [probabilities p and (1-p) associated with ferromagnetic and antiferromagnetic couplings, respectively] is studied by applying a real-space renormalization-group technique on a hierarchical lattice that approaches the square lattice. Within such a procedure, there is no spin-glass phase and only two finite-temperature phases are found, namely, the paramagnetic and ferromagnetic ones. In spite of a reasonably small computational effort, an accurate paramagnetic-ferromagnetic boundary is presented: the estimate for the slope at p=1 is in very good agreement with the well-known exact result, whereas the coordinates of the Nishimori point are determined within a high precision. Below the Nishimori point, such a boundary is not strictly vertical-contrary to the usual belief-in such a way that a small reentrance is found at low temperatures.
Nobre
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Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário, Caixa Postal 1641 59072-970 Natal, RN, Brazil. nobre@dfte.ufrn.br