83,194 research outputs found

    Geometrical Phase Transitions

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    The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.Comment: 5 pages, 3 figures, talk presented at Conference on Computational Physics 2004, Genoa, 1-4 September 2004; 2nd version: slightly expanded versio

    Topological aspects of geometrical signatures of phase transitions

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    Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure

    Geometrical aspects in the analysis of microcanonical phase-transitions

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    In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of Ï•4\phi^4 models with either nearest-neighbours and mean-field interactions

    Geometrical Expression of Excess Entropy Production

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    We derive a geometrical expression of the excess entropy production for quasi-static transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct thermodynamics of nonequilibrium steady states
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