q-state Potts model metastability study using optimized GPU-based Monte Carlo algorithms

Abstract

We implemented a GPU based parallel code to perform Monte Carlo simulations of the two dimensional q-state Potts model. The algorithm is based on a checkerboard update scheme and assigns independent random numbers generators to each thread. The implementation allows to simulate systems up to ∼ 10 9 spins with an average time per spin flip of 0.147ns on the fastest GPU card tested, representing a speedup up to 155x, compared with an optimized serial code running on a high-end CPU.The possibility of performing high speed simulations at large enough system sizes allowed us to provide a positive numerical evidence about the existence of metastability on very large systems based on Binder's criterion, namely, on the existence or not of specific heat singularities at spinodal temperatures different of the transition one.

Phenomenological theory of the Potts model evaporation-condensation transition

“…A different challenge for future research could be that of clarifying the nature of the 3D system, for which the conventional EC exponents were proposed [21]. A final controversy regarding metastability: we suggest that the thermodynamic metastable spinodal [41] can be identified with the EC transition; this would contradict the results based on the pseudo-critical divergence [42][43][44], which indicate that there is a "thermodynamic" endpoint of the metastable phase, not vanishing for large system sizes.…”

Monte Carlo Methods for Massively Parallel Computers

“…It is possible to generate a large number of "good" multipliers c such that generator instances used by different threads use different values of c. MWC can be efficiently implemented on GPU. 51 The statistical quality of this generator turns out to be only marginally better than that for the pure 32-bit LCG, see the data in Table 2, while the storage requirement is 64 bit for the state and an additional 32 bits for the multiplier c, such that the additional effort as compared to the LCGs does not seem to be worthwhile. • Lagged Fibonacci generators.…”

“…A scheme dubbed "crinkling" that ensures that three out of four neighbors are next to each other for the square lattice was proposed in Ref. [51]. A similar, but more general scheme of "slicing" for hypercubic lattices in any dimension is used in Ref.…”

FPGA Hardware Acceleration of Monte Carlo Simulations for the Ising Model

“…Despite its relative simplicity, Ising-type models and their generalizations (e.g., Potts model, see [9] and references therein) are extensively used to analyze properties of a large variety of systems exhibiting cooperative phenomena, ranging from simple ferromagnetism to complex disordered materials (e.g., spin glasses) [10]. Moreover, being originally restricted to the realm of solid state physics, they have been shown to be extremely useful in other disciplines, such as soft condensed matter (e.g.…”