Phase Diagram of the p-Spin-Interacting Spin Glass with Ferromagnetic Bias and a Transverse Field in the Infinite- p Limit

Abstract

The phase diagram of the p-spin-interacting spin glass model in a transverse field is investigated in the limit p ! 1 under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p ! 1 by using the large-p expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.

Code-division multiple-access multiuser demodulator by using quantum fluctuations

“…As these approximations may be naturally expected to be broken in the low temperature region, we should draw a so-called de Almeida-Thouless (AT) line [22], and we should also discuss the validity of SA. Although the validity of SA has been partially investigated in the quantum random energy model [23], it has not yet been investigated for Ising spin glass in a transverse field. It is generally very difficult to carry out numerical calculations involving very low temperatures with reliable numerical accuracy, and pure quantum demodulation, which is defined as QMPM without any thermal fluctuations, is also very difficult to address.…”

Simple Glass Models and Their Quantum Annealing

“…The quantum transition has been found to be first order at low temperature for all RFO models [5,6,14]. We show here first that the quantum version of the random energy model (QREM) can be solved analytically using only basic tools of perturbation theory, a derivation whose simplicity provides a detailed understanding of the quantum glass transition.…”

“…Far from the jump times, the functions q t;t 0 andq t;t 0 take the same form as those computed at those times for the glass phase [the regions ð1; 1Þ], for the quantum paramagnet [in the regions ð2; 2Þ], and are zero in the mixed regions ð1; 2Þ-ð2; 1Þ. In the large p limit the problem can be solved completely using the so-called ''static approximation'' [5,14] within the ð1; 1Þ regions, and, in addition, the fact thatq d t;t 0 andq t;t 0 become either infinity or zero, with sharp interfaces. Subsequent terms are treated similarly and give vanishing corrections so that E 0 ðÀÞ ¼ ÀNÀ À 1 2À þ oð1Þ.…”

“…Quantum SGs have been investigated over the past 30 years [12] using an elaborate mathematical formalism combining the replica [13] and the Suzuki-Trotter methods [5,14] in order to introduce disorder and quantum mechanics. The quantum transition has been found to be first order at low temperature for all RFO models [5,6,14].…”

“…Following the standard strategy [5,6,14], the trace is computed via the Suzuki-Trotter and the replica trick. One obtains an effective replicated free energy as a function of the overlaps q t;t 0 between the replicas at two (imaginary) times and some corresponding Lagrange multipliersq t;t 0 , for which a particular ansatz must be proposed [5,6].…”