Magnetic-glassy multicritical behavior of the three-dimensional±JIsing model

Abstract

We consider the three-dimensional ±J model defined on a simple cubic lattice and study its behavior close to the multicritical Nishimori point where the paramagnetic-ferromagnetic, the paramagnetic-glassy, and the ferromagnetic-glassy transition lines meet in the T -p phase diagram (p characterizes the disorder distribution and gives the fraction of ferromagnetic bonds). For this purpose we perform Monte Carlo simulations on cubic lattices of size L ≤ 32 and a finitesize scaling analysis of the numerical results. The magnetic-glassy multicritical point is found at p * = 0.76820(4), along the Nishimori line given by 2p − 1 = Tanh(J/T ). We determine the renormalization-group dimensions of the operators that control the renormalization-group flow close to the multicritical point, y 1 = 1.02(5), y 2 = 0.61(2), and the susceptibility exponent η = −0.114(3). The temperature and crossover exponents are ν = 1/y 2 = 1.64(5) and φ = y 1 /y 2 = 1.67(10), respectively. We also investigate the model-A dynamics, obtaining the dynamic critical exponent z = 5.0(5).

Critical behavior of three-dimensional Ising spin glass models

“…The coordinates of the MGP in the T -p plane are 42 T * = 1.6692(3) and p * = 0.76820 (4). The multicritical behavior is characterized by 42 the thermal exponent ν = 1.64(5), the crossover exponent φ = 1.67 (10), and the magnetic (and also overlap) exponent η = −0.114 (3).…”

“…1. The high-temperature phase is paramagnetic for any p. The nature of the low-temperature phase depends on the value of p: it is ferromagnetic for small values of 1 − p, while it is glassy with vanishing magnetization for sufficiently large values of 1 − p. The three phases are separated by transition lines, which meet at a magnetic-glassy multicritical point (MGP), usually called Nishimori point, which is located along the so-called Nishimori line 38,39,40,41,42 defined by the relation (p ≥ 1/2)…”

“…As a consequence, the Ising point p = 1 is a multicritical point 44 with crossover exponent φ = α Is , where 45 α Is = 0.1096(5) is the Ising specific-heat exponent. The critical behavior for any 1 > p > p * belongs to the randomly-dilute Ising (RDI) universality class, 44 characterized by the correlation-length critical exponent 46,47 ν = 0.683 (2) and by the magnetic exponent η = 0.036 (1). The coordinates of the MGP in the T -p plane are 42 T * = 1.6692(3) and p * = 0.76820 (4).…”

Relaxational dynamics in 3D randomly diluted Ising models

“…Here p N is the location of the magnetic-glassy Nishimori multicritical point, which has been recently computed in [35]: p N = 0.76820 (4). In this work we consider a relaxational dynamics without conserved order parameters, i.e.…”

The critical behavior of 3D Ising spin glass models: universality and scaling corrections

“…The paramagnetic-glass transition line extends for p * > p > 1 − p * , where [15] p * = 0.76820(4). For 1 > p > p * the low-temperature phase is ferromagnetic, and the transition belongs to the randomly-dilute Ising universality class [16]. We also consider a bond-diluted ±J Ising model with bond-occupation probability p b = 0.45, and equal probability for the values ±J.…”