Using a recently developed method to rigorously control the finite-size behaviour in long cylinders near first-order phase transitions, I calculate the finite-size scaling of the first q+1 eigenvalues of the transfer matrix of the q states Potts model in a d dimensional periodic box of volume L \u00d7 . . . \u00d7 L \u00d7 t (assuming that d \u2265 2 and that q is sufficiently large). I find two simple eigenvalues \u03bb\u00b1 corresponding to the trivial representation of the global symmetry and an q \u2212 1 fold degenerate eigenvalue \u03bb\u22a5 corresponding to the remaining irreducible representations of the global symmetry group. The finite-size scaling of the gap \u03be\u22121(L, \u03b2) = log(\u03bb+\/\u03bb\u22a5) and of the gap \u03be\u22121 sym(L, \u03b2) = log(\u03bb+\/\u03bb\u2212) in the symmetric subspace, and their relation to the surface tension, as well as the finite-size scaling of the internal energy Ecyl(L, \u03b2) = \u2212L\u2212(d\u22121)d log \u03bb+\/d\u03b2 are discussed. As a final application, I discuss the finite-size scaling of the derivative of \u03be(L, \u03b2). I prove that 1\/\u03bd(L) := log[\u2212Ld\u03be(L, \u03b2)\/d\u03b2]\u03b2=\u03b2t(L)\/ log L converges to the renormalization group eigenvalue yT = d, if \u03b2t(L) is chosen as the point where \u03be\u22121 sym(L, \u03b2) is minimal. I also propose other definitions of a finite volume exponent \u03bd(L) which should be more suitable for numerical considerations.<\/p>\n","protected":false},"excerpt":{"rendered":"
Using a recently developed method to rigorously control the finite-size behaviour in long cylinders near first-order phase transitions, I calculate the finite-size scaling of the first q+1 eigenvalues of the transfer matrix of the q states Potts model in a d dimensional periodic box of volume L \u00d7 . . . \u00d7 L \u00d7 t […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-318653","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Nucl. 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