An investigation of finite-size scaling for systems with long-range interaction: The spherical model |
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Authors: | Jordan G Brankov Nicholai S Tonchev |
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Institution: | (1) Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria;(2) Institute for Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria |
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Abstract: | A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr
–d –
, whered is the space dimensionality and >0. It allows for a unified treatment of short-range ( =2) and long-range ( <2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL
d–d ×
d
subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd![ges](/content/m76w1v3746m425nt/xxlarge10878.gif) , 0 d![prime](/content/m76w1v3746m425nt/xxlarge8242.gif) ![les](/content/m76w1v3746m425nt/xxlarge10877.gif) . It is shown that the -expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities. |
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Keywords: | Finite-size scaling long-range interactions spherical model -expansion" target="_blank">gif" alt="epsi" align="BASELINE" BORDER="0">-expansion |
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