Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models
arXiv:cond-mat/9906340 · doi:10.1103/PhysRevB.61.11521
Abstract
The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.
10 pages, 4 figures
References in corpus (1)
Cited by in corpus (29)
- Canonical Solution of Classical Magnetic Models with Long-Range Couplings
- Interacting damage models mapped onto Ising and percolation models
- Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution
- Phase transitions in systems with non-additive long-range interactions
- Analysis of the exactness of mean-field theory in long-range interacting systems
- A Kac-potential treatment of nonintegrable interactions
- Prethermalization in the transverse-field Ising chain with long-range interactions
- Instability of the mean-field states and generalization of phase separation in long-range interacting systems
- Evidences for Tsallis non-extensivity on CMR manganites
- Nonextensive thermodynamics of the two-site Hubbard model
- Rigidity percolation in a field
- Long-range interacting systems are locally non-interacting
- Spin glasses in the non-extensive regime
- The Origin of Mean-Field Behavior in an Elastic Ising Model
- Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems
- Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
- On the Truncation of Systems with Non-Summable Interactions
- Testing boundary conditions efficiency in simulations of long-range interacting magnetic models
- Non glassy ground-state in a long-range antiferromagnetic frustrated model in the hypercubic cell
- Complex-q zeros of the partition function of the Potts model with long-range interactions
- Scaling relations in equilibrium nonextensive thermostatistics
- Exact mean-field solution of a spin chain with short-range and long-range interactions
- Mean-field theory is exact for the random-field model with long-range interactions
- Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line
- Critical exponents for the long-range Ising chain using a transfer matrix approach
- Quantum fluctuations inhibit symmetry breaking in the HMF model
- Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions
- Mean Field in Long-Range Ferromagnets and Periodic Boundary Conditions
- Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics