Abstract
A large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered. The dependence of the finite-volume magnetizationM per(h, L) in cubes of sizeL dunder periodic boundary conditions on the external fieldh is analyzed. For the case where two phases coexist at the infinite-volume transition pointh t , we prove that, independent of the details of the model, the finite-volume magnetization per lattice site behaves likeM per(h t )+M tanh[ML d(h−ht)] withM per(h) denoting the infinite-volume magnetization and M=1/2[M per(h t +0)−M per(h t −0)]. Introducing the finite-size transition pointh m (L) as the point where the finite-volume susceptibility attains the maximum, we show that, in the case of asymmetric field-driven transitions, its shift ish t −h m (L)=O(L −2d), in contrast to claims in the literature. Starting from the obvious observation that the number of stable phases has a local maximum at the transition point, we propose a new way of determining the pointh t from finite-size data with a shift that is exponentially small inL. Finally, the finite-size effects are discussed also in the case where more than two phases coexist.
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On leave from: Institut für Theoretische Physik, FU-Berlin, D-1000 Berlin 33, Federal Republic of Germany.
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Borgs, C., Kotecký, R. A rigorous theory of finite-size scaling at first-order phase transitions. J Stat Phys 61, 79–119 (1990). https://doi.org/10.1007/BF01013955
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DOI: https://doi.org/10.1007/BF01013955