Multiple singularities of the equilibrium free energy in a one-dimensional model of soft rods
| Autor: | Tridib Sadhu, Sushant Saryal, Deepak Dhar, Juliane U. Klamser |
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| Rok vydání: | 2018 |
| Předmět: |
Coupling constant
Physics Infinite number Statistical Mechanics (cond-mat.stat-mech) General Physics and Astronomy Inverse temperature FOS: Physical sciences 01 natural sciences Rod 010305 fluids & plasmas Lattice constant Lattice (order) 0103 physical sciences Gravitational singularity 010306 general physics Condensed Matter - Statistical Mechanics Mathematical physics Counterexample |
| DOI: | 10.48550/arxiv.1806.09841 |
| Popis: | There is a misconception, widely shared amongst physicists, that the equilibrium free energy of a one-dimensional classical model with strictly finite-ranged interactions, and at non-zero temperatures, can not show any singularities as a function of the coupling constants. In this Letter, we discuss an instructive counter-example. We consider thin rigid linear rods of equal length $2 \ell$ whose centers lie on a one-dimensional lattice, of lattice spacing $a$. The interaction between rods is a soft-core interaction, having a finite energy $U$ per overlap of rods. We show that the equilibrium free energy per rod $\mathcal{F}(\tfrac{\ell}{a}, \beta)$, at inverse temperature $\beta$, has an infinite number of singularities, as a function of $\tfrac{\ell}{a}$. Comment: 5 pages with additional 4 pages of supplemental material |
| Databáze: | OpenAIRE |
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