Multipath Metropolis simulation: An application to the classical Heisenberg model

Abstract

Processor cores are becoming less expensive and thus more accessible. To utilize increasing number of available computing elements, good parallel algorithms are necessary. In light of these changes in contemporary computing, multipath Metropolis simulation of classical Heisenberg model is explored. In contrast to the original single-path algorithm, multipath simulation approach is inherently parallel because different random-walk paths are mutually independent. This independence enables easy and efficient harnessing of numerous cores' computing power in embarrassingly parallel algorithms. Aside form being inherently parallel, multipath simulation approach results in independent and normally distributed simulation output. Normal distribution enables simple and straightforward statistical processing. Thus, multipath simulation results can be easily computed with arbitrary and statistically known precision.

Thermodynamic Properties of Heisenberg Spin Systems

“…The Monte Carlo (MC) simulation is one of the fundamental methods of statistical physics, particularly in the study of phase transitions and magnetic phenomena [6,7,8]. We used the modified Metropolis algorithm: our variant of the Multipath Metropolis (MM) simulation is used which was based on [9]. Unlike the standard single-path algorithm, the Metropolis algorithm applied to multiple random-walk paths is initially better for parallelization.…”

Verification of a New Quantum Simulation Approach through Its Application to Heisenberg-Like Models

“…Even nowadays, the Heisenberg model is still a very hot research topic which are currently intensively studied both theoretically with quantum physics [1][2][3][4][5] and numerically mainly with Monte Carlo (MC) method [6][7][8][9][10]. However, the MC method is based on classical physics, since all spins in the studied systems are treated by the method as classical vectors with fixed lengths, though they are allowed to rotate spatially in the computing process.…”