Study of ±J Ising Spin Glasses via Multicanonical Ensemble

We performed numerical simulations of 2D and 3D Edwards-Anderson spin glass models by using the recently developed multicanonical ensemble. Our ergodicity times increase with the lattice size approximately as V 3. The energy, entropy and other physical quantities are easily calculable at all temperatures from a single simulation. Their finite size scalings and the zero temperature limits are also explored. The low temperature phase of the spin glasses has distinct properties like broken ergodicity and the absence of self-averaging, which in turn make their numerical investigation an extremely difficult task [1]. For temperatures below a bifurcation point, the spin glass configuration space is supposed to split off into a number of valleys which are separated by high energy barriers. Due to the exponentially increasing relaxation times [2] encountered in canonical simulations, tunneling between these many thermodynamics states becomes almost impossible. Recent simulations [3] of the 3D Edwards-Anderson model in a magnetic field seem to support the mean field picture [4] rather than the alternative droplet model [5], but it can be argued that equilibrium at sufficiently low temperatures has not been reached [6]. One of the simplest spin glass systems is described by the Edwards-Anderson Hamiltonian H = − ∑ Jijsisj, (1) where the sum includes only the nearest neighbours and the exchange interactions Jij = ±1 between the spins si = ±1 are the quenched random variables. The constraint ∑ Jij = 0 is imposed for each realization. We present a new approach to spin glass simulations which reduces the exponential slowing to a power law and enables one to sample independent ground states in one simulation. This is achieved by exploiting the multicanonical ensemble [7]. Supercomputer Computations Research Institute, Florida State University,Tallahassee,FL 32306,USA Department of Physics Engineering, Hacettepe University, 06532 Beytepe, Ankara, Turkey Department of Physics, Florida State University, Tallahassee, FL 32306, USA Wissenschaftskolleg zu Berlin, Wallotstr. 19, Berlin 33, Germany ∗To appear in the Proceedings of the Sixth Annual Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics, 22–26 Feb. 1993, Athens, Georgia.