Polylogarithm Identities in a Conformal Field Theory in Three Dimensions

The $N=\infty$ vector $O(N)$ model is a solvable, interacting field theory in three dimensions ($D$). In a recent paper with A. Chubukov and J. Ye~\cite{self}, we have computed a universal number, $\tilde{c}$, characterizing the size dependence of the free energy at the conformally-invariant critical point of this theory. The result~\cite{self} for $\tilde{c}$ can be expressed in terms of polylogarithms. Here, we use non-trivial polylogarithm identities to show that $\tilde{c}/N = 4/5$, a rational number; this result is curiously parallel to recent work on dilogarithm identities in $D=2$ conformal theories. The amplitude of the stress-stress correlator of this theory, $c$ (which is the analog of the central charge), is determined to be $c/N=3/4$, also rational. Unitary conformal theories in $D=2$ always have $c = \tilde{c}$; thus such a result is clearly not valid in $D=3$.Comment: LATEX, 7 page

FAUNA BURUANA HETEROPTERA, FAM. PYRRHOCORIDAE.

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String effects in Polyakov loop correlators

We compare the predictions of the effective string description of confinement in finite temperature gauge theories to high precision Monte Carlo data for the three-dimensional Z(2) gauge theory. We show that string interaction effects become more relevant as the temperature is increased towards the deconfinement one, and are well modeled by a Nambu-Goto string action.Comment: Lattice2002(nonzerot

Alternating linear-chain antiferromagnetism in copper nitrate Cu(NO\u3csub\u3e3\u3c/sub\u3e)\u3csub\u3e2\u3c/sub\u3e.2.5 H\u3csub\u3e2\u3c/sub\u3eO

Current interest in the behavior of Heisenberg alternating antiferromagnetic quantum chains has been stimulated by the discovery of an unusual class of magnetoelastic spin-Peierls systems. Copper nitrate, Cu(NO3)2.2.5 H2O, does not display a spin-Peierls transition, but its dominant magnetic behavior is that of a strongly alternating antiferromagnetic chain with temperature-independent alternation. A remarkable, simultaneous fit is demonstrated between theoretical studies and a wide variety of zero- (low-) field experimental measurements, including susceptibility, magnetization, and specific heat. The fitting parameters are α(degree of alternation) = 0.27, J1/k=2.58 K, gb=2.31, and g⊥=2.11. Slight systematic discrepancies are attributed to weak interchain coupling. Theoretical studies also predict a rich variety of behavior in high fields, particularly in the region involving the lower and upper critical fields, Hc1 = 28 kOe and Hc2 = 44 kOe. Experimental specific-heat measurements at H = 28.2 and 35.7 kOe show quantitative agreement with theory in this interesting parameter region. The fitting parameters are the same as for zero field and, again, small discrepancies between theory and experiment may be attributed to interchain coupling. The exceptional magnetic characterization of copper nitrate suggests its use for further experimental study in the vicinity of the high-field ordering region

GPU accelerated Monte Carlo simulations of lattice spin models

We consider Monte Carlo simulations of classical spin models of statistical mechanics using the massively parallel architecture provided by graphics processing units (GPUs). We discuss simulations of models with discrete and continuous variables, and using an array of algorithms ranging from single-spin flip Metropolis updates over cluster algorithms to multicanonical and Wang-Landau techniques to judge the scope and limitations of GPU accelerated computation in this field. For most simulations discussed, we find significant speed-ups by two to three orders of magnitude as compared to single-threaded CPU implementations.Comment: 5 pages, 4 figures, 1 table; Physics Procedia 15, 92 (2011

Self-Similar Crossover in Statistical Physics

An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar approximation theory, being its variant where control functions are defined from asymptotic crossover conditions. Several examples from statistical physics demonstrate that the suggested method results in rather simple and surprisingly accurate formulae.Comment: 1 file, 23 pages, LaTe