A Kac-potential treatment of nonintegrable interactions
arXiv:cond-mat/0009031 · doi:10.1103/PhysRevE.63.031108
Abstract
We consider d-dimensional systems with nonintegrable, algebraically decaying pairwise interactions. It is shown that, upon introduction of periodic boundary conditions and a long-distance cutoff in the interaction range, the bulk thermodynamics can be obtained rigorously by means of a Kac-potential treatment, leading to an exact, mean-field-like theory. This explains various numerical results recently obtained for finite systems in the context of ``nonextensive thermodynamics,'' and in passing exposes a strong regulator dependence not discussed in these studies. Our findings imply that, contrary to some claims, Boltzmann-Gibbs statistics are sufficient for a standard description of this class of nonintegrable interactions.
RevTeX, 8 pages, 1 figure
References in corpus (11)
- Negative Specific Heat in Astronomy, Physics and Chemistry
- Classical critical behavior of spin models with long-range interactions
- Long-range interacting rotators: connection with the mean--field approximation
- Long-range interactions and non-extensivity in ferromagnetic spin models
- Ginzburg Criterion for Coulombic Criticality
- Thermodynamic Limit for Dipolar Media
- Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models
- Critical Temperature and Nonextensivity in Long-range Interacting Lennard-Jones-like Fluids
- Phase diagram of a stochastic cellular automaton with long-range interactions
- Comment on ``Scaling Laws for a System with Long-Range Interactions within Tsallis Statistics''
- Correlations in Ising chains with non-integrable interactions
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- Microcanonical solution of lattice models with long range interactions
- The Origin of Mean-Field Behavior in an Elastic Ising Model
- Caloric Curves in two and three-dimensional Lennard-Jones-like systems including Long-range forces
- Nonextensive scaling in a long-range Hamiltonian system
- Inverse Ising problem for one-dimensional chains with arbitrary finite-range couplings
- On the Truncation of Systems with Non-Summable Interactions
- Testing boundary conditions efficiency in simulations of long-range interacting magnetic models
- Comment on "Black Hole Entropy: A Closer Look"
- Exact mean-field solution of a spin chain with short-range and long-range interactions
- Scaling relations in equilibrium nonextensive thermostatistics
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- Mass transport perspective on an accelerated exclusion process: Analysis of augmented current and unit-velocity phases
- Mean Field in Long-Range Ferromagnets and Periodic Boundary Conditions
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