Parallel tempering simulation of the three-dimensional Edwards–Anderson model with compact asynchronous multispin coding on GPU

Abstract

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional 28.4% speedup compared with the traditionally used Asynchronous Multispin Coding (AMSC). Our overall design sustains a performance of 33.5 picoseconds per spin flip attempt for simulating the three-dimensional Edwards-Anderson model with parallel tempering, which significantly improves the performance over existing GPU implementations.

GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice

“…It takes a lot of thought and caution to incorporate all of this to create a highly optimized CUDA program. The use of GPGPU for scientific applications is of interest for instance in the stochastic simulations of spin models [1][2][3][4]. Our main goal is to incorporate the GPU-accelerated computing in the population annealing (PA) method proposed by Hukushima and Iba [5].…”

Monte Carlo Methods for Massively Parallel Computers

“…In both cases, only a single integer or floating-point variable needs to be communicated. j Parallel tempering has been implemented on GPU for a range of systems, including spin models, 36 polymers, 107 as well as spin glasses 50,52,108 and random field systems. 109 In terms of the work distribution, the actual replica-exchange step is so light that it is typically irrelevant whether it is implemented on CPU or in a GPU kernel.…”

“…The main focus has been on systems with discrete spins such as Ising and Potts spin glasses, where the Ising case corresponds to the Hamiltonian (7) with couplings J ij typically drawn from a Gaussian or a bimodal distribution. A number of different implementations on GPU each use some mixture of the same general ingredients: 36,50,52 parallel tempering, checkerboard updates and tiling, multi-spin coding across different disorder realizations, m carefully tailored setups for random-number generation. Some attention has also been paid to systems with continuous degrees of freedom, in particular the Heisenberg spin glass, where the exceptional floating-point performance of current GPUs can be brought to the fore, in particular if single-precision variables are used for the spins and the special-function units can be employed.…”

GPU accelerated population annealing algorithm

“…Quite efficient bitwise operations are available to implement a parallel Metropolis update of the spins coded in a p-bit word. This approach has been extensively used in simulations, in particular, of spin-glass models [23,[38][39][40][41].…”

“…This is illustrated in the data in the first section of Table 1, where a different random number is drawn using the base generator for each of the p spins coded in a word, i.e., n RNG = p. The relatively moderate and mostly p independent improvement is a result of the fact that the time taken per spin update is in this setup limited by the time it takes to generate the random numbers used to decide about the acceptance of spin flips. A number of implementations of this scheme for spin glasses [23,39,40] have used the same random number for deciding about flipping all of the p spins in a word. This introduces some correlations, however, and while it is argued that this effect is minor for spin-glass problems due to the property of bond chaos in such systems [42], we expect it to be much more relevant for the case of the ferromagnet studied here.…”