TY - JOUR
T1 - Optimization of finite-size errors in finite-temperature calculations of unordered phases
AU - Iyer, Deepak
AU - Srednicki, Mark
AU - Rigol, Marcos
N1 - Publisher Copyright:
© 2015 American Physical Society.
PY - 2015/6/29
Y1 - 2015/6/29
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.91.062142
DO - 10.1103/PhysRevE.91.062142
M3 - Article
C2 - 26172696
AN - SCOPUS:84936971012
SN - 1539-3755
VL - 91
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 6
M1 - 062142
ER -