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Register a new userCharacterization and Efficient Monte Carlo Sampling of Disordered Microphases
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The disordered microphases that develop in the high-temperature phase of systems with competing short-range attractive and long-range repulsive (SALR) interactions result in a rich array of distinct morphologies, such as cluster, void cluster and percolated (gel-like) fluids. These different structural regimes exhibit complex relaxation dynamics with significant relaxation heterogeneity and slowdown. The overall relationship between structure and configurational sampling schemes, however, remains largely uncharted. In this article, the disordered microphases of a schematic SALR model are thoroughly characterized, and structural relaxation functions adapted to each regime are devised. The sampling efficiency of various advanced Monte Carlo (MC) sampling schemes--Virtual-Move (VMMC), Aggregation-Volume-Bias (AVBMC) and Event-Chain (ECMC)--is then assessed. A combination of VMMC and AVBMC is found to be computationally most efficient for cluster fluids and ECMC to become relatively more efficient as density increases. These results offer a complete description of the equilibrium disordered phase of a simple microphase former as well as dynamical benchmarks for other sampling schemes.
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Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the general theory enabling infinite-order automatic differentiation on expectations computed by Monte Carlo with unnormalized probability distributions, which we call automatic differentiable Monte Carlo (ADMC). By implementing ADMC algorithms on computational graphs, one can also leverage state-of-the-art machine learning frameworks and techniques to traditional Monte Carlo applications in statistics and physics. We illustrate the versatility of ADMC by showing some applications: fast search of phase transitions and accurately finding ground states of interacting many-body models in two dimensions. ADMC paves a promising way to innovate Monte Carlo in various aspects to achieve higher accuracy and efficiency, e.g. easing or solving the sign problem of quantum many-body models through ADMC.
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