2,541 research outputs found

    Perturbative nonequilibrium dynamics of phase transitions in an expanding universe

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    A complete set of Feynman rules is derived, which permits a perturbative description of the nonequilibrium dynamics of a symmetry-breaking phase transition in λϕ4\lambda\phi^4 theory in an expanding universe. In contrast to a naive expansion in powers of the coupling constant, this approximation scheme provides for (a) a description of the nonequilibrium state in terms of its own finite-width quasiparticle excitations, thus correctly incorporating dissipative effects in low-order calculations, and (b) the emergence from a symmetric initial state of a final state exhibiting the properties of spontaneous symmetry breaking, while maintaining the constraint 0\equiv 0. Earlier work on dissipative perturbation theory and spontaneous symmetry breaking in Minkowski spacetime is reviewed. The central problem addressed is the construction of a perturbative approximation scheme which treats the initial symmetric state in terms of the field ϕ\phi, while the state that emerges at later times is treated in terms of a field ζ\zeta, linearly related to ϕ2\phi^2. The connection between early and late times involves an infinite sequence of composite propagators. Explicit one-loop calculations are given of the gap equations that determine quasiparticle masses and of the equation of motion for and the renormalization of these equations is described. The perturbation series needed to describe the symmetric and broken-symmetry states are not equivalent, and this leads to ambiguities intrinsic to any perturbative approach. These ambiguities are discussed in detail and a systematic procedure for matching the two approximations is described.Comment: 22 pages, using RevTeX. 6 figures. Submitted to Physical Review

    An Analytic Equation of State for Ising-like Models

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    Using an Environmentally Friendly Renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, y=f(x)y=f(x), that exhibits all desired asymptotic and analyticity properties in the three limits x0x\to 0, xx\to \infty and x1x\to -1. The only necessary inputs are the Wilson functions γλ\gamma_\lambda, γϕ\gamma_\phi and γϕ2\gamma_{\phi^2}, associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N=1, we derive a one-loop equation of state for 2<d<42< d<4 naturally parameterized by a ratio of non-linear scaling fields. For d=3d=3 we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure
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