Long-range interactions and non-extensivity in ferromagnetic spin models

Abstract

The Ising model with ferromagnetic interactions that decay as $1/r^{\alpha }$ is analyzed in the non-extensive regime $0\le \alpha \le d$, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model in the $N\to \infty$ limit ($N$ being the number of spins) we propose a generalization of the Curie-Weiss model, for which the $N\to \infty$ limit is well defined for all $\alpha \ge 0$. We conjecture that mean field theory is {\it exact} in the last model for all $0\le \alpha \le d$. This conjecture is supported by Monte Carlo heat bath simulations in the $d=1$ case. Moreover, we confirm a recently conjectured scaling (Tsallis\cite{Tsallis}) which allows for a unification of extensive ($\alpha >d$) and non-extensive ($0\le \alpha \le d$) regimes.

RevTex, 12 pages, 1 eps figure

References in corpus (1)

• Correlations in Ising chains with non-integrable interactions

Cited by in corpus (60)

• Black hole thermodynamical entropy
• Entanglement entropy for the long range Ising chain
• Generalized algebra within a nonextensive statistics
• Long-range interacting rotators: connection with the mean--field approximation
• Power-Law Sensitivity to Initial Conditions within a Logistic-like Family of Maps: Fractality and Nonextensivity
• Chimera patterns induced by distance-dependent power-law coupling in ecological networks
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Real-time dynamics of string breaking in quantum spin chains
• Influence of the interaction range on the thermostatistics of a classical many-body system
• Canonical Solution of Classical Magnetic Models with Long-Range Couplings
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• Analytical results for coupled map lattices with long-range interactions
• Is Tsallis thermodynamics nonextensive?
• Interacting damage models mapped onto Ising and percolation models
• Random transverse-field Ising chain with long-range interactions
• Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models
• Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution
• Reply to Comment on "Towards a large deviation theory for strongly correlated systems"
• Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space
• A Kac-potential treatment of nonintegrable interactions
• On the generalized entropy pseudoadditivity for complex systems
• Increased persistence via asynchrony in oscillating ecological populations with long-range interaction
• Long-range random transverse-field Ising model in three dimensions
• Critical Temperature and Nonextensivity in Long-range Interacting Lennard-Jones-like Fluids
• Monte Carlo Simulation of Magnetic System in the Tsallis Statistics
• Correct thermodynamic forces in Tsallis Thermodynamics: connection with Hill Nanothermodynamics
• Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States
• Many-body enhancement in a spin-chain quantum heat engine
• Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature
• Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics
• Self-organized criticality in a model of biological evolution with long range interactions
• Fast Flat-Histogram Method for Generalized Spin Models
• Ferromagnetism in one dimension: Critical Temperature
• Effects of energy extensivity on the quantum phases of long-range interacting systems
• Inter-occurrence times and universal laws in finance, earthquakes and genomes
• Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions
• Long-range interacting solitons: pattern formation and nonextensive thermostatistics
• Thermostatistics of extensive and non-extensive systems using generalized entropies
• Dynamical robustness of complex networks subject to long-range connectivity
• Nonextensive scaling in a long-range Hamiltonian system
• Phase diagram of a stochastic cellular automaton with long-range interactions
• Topological Non--connectivity Threshold in long-range spin systems
• On the Truncation of Systems with Non-Summable Interactions
• Synchronization in large populations of limit cycle oscillators with long-range interactions
• Thermodynamics from a scaling Hamiltonian
• Phase-transitions of the random bond Potts chain with long-range 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
• Quantum Corrections for Generalized Partition Functions
• Scaling relations in equilibrium nonextensive thermostatistics
• Effects of long range hopping in the Bose-Hubbard model
• On the extended Kolmogorov-Nagumo information-entropy theory, the q -> 1/q duality and its possible implications for a non-extensive two dimensional Ising model
• Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps
• Making thermodynamic functions of nanosystems intensive
• Critical exponents for the long-range Ising chain using a transfer matrix approach
• Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions
• Enhancement of magnetic anisotropy barrier in long range interacting spin systems
• Universal behavior in the static and dynamic properties of the $\alpha$-XY model
• Observation of complex functional cortical patterns in brain cognition
• Mean Field in Long-Range Ferromagnets and Periodic Boundary Conditions