Replica symmetry breaking in a quantum spin system with random fields

Soluble model to treat the quantum spin glass

“…It is, however, qualitatively similar to the ones recently obtained using the quantum spherical description to treat the Ising spin glass in a transverse field. 3 Our results do not agree with those from pair approximation, 6 Monte Carlo simulation, 19 and renormalization group 5 which predict an increase of T c for small fields ⍀. The corresponding quantum-critical point above which no spin-glass transition occurs in the present model reads ␦ c ϭ1.…”

“…19͒ has been verified by some Monte Carlo simulation. 19 The first step of replica-symmetry-breaking ͑RSB͒ solution 20 in the infiniterange Ising spin glass with a transverse field ͑quantum spin glass͒ has showed that the phase diagram is not in accordance with the results of pair approximation 6 and Monte Carlo simulation. 19 On the other hand, to treat the influence of the transverse field in the spin-glass phase, we generalize in this paper the van Hemmen model of spin glass, which consists of a fully connected net of N Ising spins with a transverse field described by the following Hamiltonian:…”

“…1 Recently, there has been growing interest in theoretical and experimental investigations of the Ising spin glass in a transverse field to treat the phase transition in quantum spin glasses. [2][3][4][5][6] Experimentally, results for the nonlinear susceptibility provide strong evidence for a finite transition temperature, T c , and as an example we have the so-called proton glasses, 7,8 being a random mixture of ferroelectric and antiferroeletric materials such as Rb 1Ϫx (NH 4 ) x H 2 PO 4 , where proton tunneling in the glass state can be represented by transverse field in the pseudospin Ising model. 9 The transverse Ising spin-glass model has also been used to treat the quantum spin-glass phase transition of the diluted dipole coupled magnet LiHo x Y 1Ϫx F 4 .…”