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arXiv · 1206.1677

Monte Carlo estimates of thermal averages and analytic continuation

Sharif D. Kunikeev·Kwang S. Kim
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Abstract

The Monte Carlo (MC) estimates of thermal averages are usually functions of system control parameters $λ$, such as temperature, volume, interaction couplings, etc. Given the MC average at a set of prescribed control parameters $λ_{0}$, the problem of analytic continuation of the MC data to $λ$-values in the neighborhood of $λ_{0}$ is considered in both classic and quantum domains. The key result is the theorem that links the differential properties of thermal averages to the higher-order cumulants. The theorem and analytic continuation formulas expressed via higher-order cumulants are numerically tested on the classical Lennard-Jones cluster system of N=13, 55, and 147 neon particles.

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Sharif D. Kunikeev, Kwang S. Kim. 2012-06-08. Monte Carlo estimates of thermal averages and analytic continuation. https://arxiv.org/abs/1206.1677

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