Optimization of finite-size errors in finite-temperature calculations of unordered phases

Abstract

It is common knowledge that the microcanonical, canonical, and grand-canonical ensembles are equivalent in thermodynamically large systems. Here, we study finite-size effects in the latter two ensembles. We show that contrary to naive expectations, finite-size errors are exponentially small in grand canonical ensemble calculations of translationally invariant systems in unordered phases at finite temperature. Open boundary conditions and canonical ensemble calculations suffer from finite-size errors that are only polynomially small in the system size. We further show that finite-size effects are generally smallest in numerical linked cluster expansions. Our conclusions are supported by analytical and numerical analyses of classical and quantum systems.

9 pages, 5 figures, published version, includes modifications to reflect errata

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• A Short Introduction to Numerical Linked-Cluster Expansions
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
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