Abstract:Relying on the recently proposed multicanonical algorithm, we present a numerical simulation of the first order phase transition in the 2d 10-state Potts model on lattices up to sizes 100 × 100. It is demonstrated that the new algorithm lacks an exponentially fast increase of the tunneling time between metastable states as a function of the linear size L of the system. Instead, the tunneling time diverges approximately proportional to L 2.65 . Thus the computational effort as counted per degree of freedom for generating an independent configuration in the unstable region of the model rises proportional to V 2.3 , where V is the volume of the system. On our largest lattice we gain more than two orders of magnitude as compared to a standard heat bath algorithm. As a first physical application we report a high precision computation of the interfacial tension.

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We present high-accuracy calculations of the density of states using multicanonical methods for lattice gauge theory with a compact gauge group U (1) on 4 4 , 6 4 and 8 4 lattices. We show that the results are consistent with weak and strong coupling expansions. We present methods based on Chebyshev interpolations and Cauchy theorem to find the (Fisher's) zeros of the partition function in the complex β = 1/g 2 plane. The results are consistent with reweighting methods whenever the latter are accurate. We discuss the volume dependence of the imaginary part of the Fisher's zeros, the width and depth of the plaquette distribution at the value of β where the two peaks have equal height. We discuss strategies to discriminate between first and second order transitions and explore them with data at larger volume but lower statistics. Higher statistics and even larger lattices are necessary to draw strong conclusions regarding the order of the transition.

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