Abstract
We consider the random-bond ±J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T *=0.9527(1), p *=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T≈0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T<T *, that the transitions are continuous and controlled by a strong-disorder fixed point with critical exponents ν=1.50(4), η=0.128(8), and β=0.095(5). This fixed point is definitely different from the Ising fixed point controlling the paramagnetic-ferromagnetic transitions for T>T *. Our results for the critical exponents are consistent with the hyperscaling relation 2β/ν−η=d−2=0.
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Parisen Toldin, F., Pelissetto, A. & Vicari, E. Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice ±J Ising Model. J Stat Phys 135, 1039–1061 (2009). https://doi.org/10.1007/s10955-009-9705-5
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DOI: https://doi.org/10.1007/s10955-009-9705-5