Optical Potts machine through networks of three-photon down-conversion oscillators

In recent years, there has been a growing interest in optical simulation of lattice spin models for applications in unconventional computing. Here, we propose optical implementation of a three-state Potts spin model by using networks of coupled parametric oscillators with phase tristability. We first show that the cubic nonlinear process of spontaneous three-photon down-conversion is accompanied by a tristability in the phase of the subharmonic signal between three states with 2π/3 phase contrast. The phase of such a parametric oscillator behaves like a three-state spin system. Next, we show that a network of dissipatively coupled three-photon down-conversion oscillators emulates the three-state planar Potts model. We discuss potential applications of the proposed system for all-optical optimization of combinatorial problems such as graph 3-COL and MAX 3-CUT.

Fractons

Fracton phases constitute a new class of quantum state of matter. They are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics or mobile only in certain directions. These phases do not wholly fit into any of the existing paradigms but connect to areas including glassy quantum dynamics, topological order, spin liquids, elasticity theory, quantum information theory, and gravity. We begin by discussing gapped fracton phases, which may be described using exactly solvable lattice spin models. We then introduce the framework of tensor gauge theory, which provides a powerful complementary perspective and allows us to access gapless fracton phases. We discuss the basic properties of gapless fracton phases and their connections to elasticity theory and gravity. We also discuss what is known about the dynamics and thermodynamics of fractons at nonzero density before concluding with a brief survey of some open problems.

Field effects on inversion walls in nematic films: A computer simulation study

Monte Carlo simulations of lattice spin models are employed to investigate the effects of an external field on the creation and evolution of inversion walls in nematic films with conical boundary conditions. The simulations, based on the well known Lebwohl-Lasher potential, allow to produce simulated polarized microscopy images which are followed during their evolution when the field is applied.

SIMULATING SPIN MODELS ON GPU: A TOUR

The use of graphics processing units (GPUs) in scientific computing has gathered considerable momentum in the past five years. While GPUs in general promise high performance and excellent performance per Watt ratios, not every class of problems is equally well suitable for exploiting the massively parallel architecture they provide. Lattice spin models appear to be prototypic examples of problems suitable for this architecture, at least as long as local update algorithms are employed. In this review, I summarize our recent experience with the simulation of a wide range of spin models on GPU employing an equally wide range of update algorithms, ranging from Metropolis and heat bath updates, over cluster algorithms to generalized ensemble simulations.