A pre-computation method sets penalization weights for constrained QUBO problems with provable guarantees for Gibbs solvers and polynomial scaling for many problem classes.
Exchange Monte Carlo Method and Application to Spin Glass Simulations
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We propose an efficient Monte Carlo algorithm for simulating a ``hardly-relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional $\pm J$ Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Monte Carlo simulations on lattices up to 48 cubed produce estimates of critical exponents for the 3D dipolar universality class, confirm a continuous phase transition, and show restoration of rotation invariance.
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Scalable Determination of Penalization Weights for Constrained Optimizations on Approximate Solvers
A pre-computation method sets penalization weights for constrained QUBO problems with provable guarantees for Gibbs solvers and polynomial scaling for many problem classes.
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A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions
Monte Carlo simulations on lattices up to 48 cubed produce estimates of critical exponents for the 3D dipolar universality class, confirm a continuous phase transition, and show restoration of rotation invariance.