Abstract
We consider the cylindrical geometry and perform MC simulations for the 3d Ising model, the 3d 3-state Potts model, 4d SU(2) and SU(3) pure gauge theory. The correlation length, defined as ξ = In( λ 0 λ 1 ) where λ 0 and λ 1 are the two largest eigenvalues of the transfer matrix, is calculated with high precision. Nightingale's finite size scaling analysis is carried out for each model. In case of second order phase transitions (Ising and SU(2)), we find the critical exponent ν determined with convincing convergence. In contrast, when the transition is (supposed to be) first order (Potts and SU(3)), the convergence is bad and results for ν remain inconclusive.
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