When topology triggers a phase transition |
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| Institution: | 1. Dipartimento di Física, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy;2. Dipartimento di Física, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy;3. INFN and Dipartimento di Física, Università di Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy;1. Grupo de Nanomateriales, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile;2. Departamento de Ciencias Físicas, Facultad de Ciencias Exactas, Universidad Andrés Bello, Santiago, Chile;1. School of Physics and Electrical Information Science, Shangqiu Normal University, Shangqiu 476000, China;2. School of Aerospace, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only possible such mechanism. Two examples of systems in which the phase transition is not accompanied by a such topology change are discussed. The first one is a model with long-range interactions, namely the mean-field -model, the second example is a one-dimensional system with a non-confining potential energy function. For both these systems, the thermodynamic singularity is generated by a maximization over one variable (or one discrete index) of a smooth function, although the context in which the maximization occurs is very different. |
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