Nature and number of distinct phases in the random field Ising model

We investigate the phase structure of the random-field Ising model with a bimodal random field distribution. Our aim is to test for the possibility of an equilibrium spin-glass phase, and for replica symmetry breaking (RSB) within such a phase. We study a low-temperature region where the spin-glass phase is thought to occur, but which has received little numerical study to date. We use the exchange Monte-Carlo technique to acquire equilibrium information about the model, in particular the $P(q)$ distribution and the spectrum of eigenvalues of the spin-spin correlation matrix (which tests for the presence of RSB). Our studies span the range in parameter space from the ferromagnetic to the paramagnetic phase. We find however no convincing evidence for any equilibrium glass phase, with or without RSB, between these two phases. Instead we find clear evidence (principally from the $P(q)$ distribution) that there are only two phases at this low temperature, with a discontinuity in the magnetization at the transition like that seen at other temperatures.Comment: 10 pages, 8 figures, submitted to PRB, original submission had fig4 and fig5 not readable. No changes have been mad

Simulating `Complex' Problems with Quantum Monte Carlo

We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and can be used to reduce statistical noise in the simulation. Furthermore, it is found that noise can be greatly reduced by approximate cancellations between the phases of the (gauge dependent) statistical flux and the external magnetic flux.Comment: Revtex, 11 pages. 3 postscript files for figures attache

Nature of ergodicity breaking in ising spin glasses as revealed by correlation function spectral properties

In this Letter we address the nature of broken ergodicity in the low temperature phase of ising spin glasses by examining spectral properties of spin correlation functions C-ij drop (SiSj). We argue that more than one extensive {[}i.e., O(N)] eigenvalue in this matrix signals replica symmetry breaking. Monte Carlo simulations of the infinite-range ising spin-glass model, above and below the almeida-thouless line, support this conclusion. exchange monte carlo simulations for the short-range model in four dimensions find a single extensive eigenvalue and a large subdominant eigenvalue consistent with droplet model expectations