Crossover from extensive to nonextensive behavior driven by long-range interactions

Jund, Philippe; Kim, Seong‐Gon; Tsallis, Constantino

doi:10.1103/physrevb.52.50

Cited by 103 publications

(93 citation statements)

References 30 publications

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“…More precisely, a convenient scale for the mean energy per spin in a finite system of size N is given by [18]:…”

Section: Exact Enumerationmentioning

confidence: 99%

Thermostatistics of extensive and non-extensive systems using generalized entropies

Salazar¹,

Toral²

2001

Physica A: Statistical Mechanics and its Applications

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We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a large number of degrees of freedom, and both short-range and long-range interactions. The first method is quite general and it is based on the numerical evaluation of the density of states with a given energy. The second method is more specific for Tsallis thermostatistics and it is based on a standard Monte Carlo Metropolis algorithm along with a numerical integration procedure. We show here that both methods are robust and efficient. We present results of the application of the methods to the one-dimensional Ising model both in a short-range case and in a long-range (non-extensive) case. We show that the thermodynamic potentials for different values of the system size N and different values of the non-extensivity parameter q can be described by scaling relations which are an extension of the ones holding for the Boltzmann-Gibbs statistics (q = 1). Finally, we discuss the differences in using standard or non-standard mean value definitions in the Tsallis thermostatistics formalism and present a microcanonical ensemble calculation approach of the averages.

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“…More precisely, a convenient scale for the mean energy per spin in a finite system of size N is given by [18]:…”

Section: Exact Enumerationmentioning

confidence: 99%

Thermostatistics of extensive and non-extensive systems using generalized entropies

Salazar¹,

Toral²

2001

Physica A: Statistical Mechanics and its Applications

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show abstract

“…[1][2][3], among many others, and references therein). In other words, if the effective range of the interactions between the constituent particles decays slowly enough with the distance, the free energy F = −β ln Z, with Z ≡ T r exp(−β H) (H being the Hamiltonian of the system and β ≡ k B T ) will grow faster than the number N of microscopic elements when N → ∞ and the so-called thermodynamic limit will be not defined.…”

mentioning

confidence: 99%

Long-range interactions and nonextensivity in ferromagnetic spin models

1996

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The Ising model with ferromagnetic interactions that decay as 1/r α is analyzed in the non-extensive regime 0 ≤ α ≤ d, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model in the N → ∞ limit (N being the number of spins) we propose a generalization of the Curie-Weiss model, for which the N → ∞ limit is well defined for all α ≥ 0. We conjecture that mean field theory is exact in the last model

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“…The situation changes in 3D systems where U͑N , T =0͒ / N scales logarithmically according to [25][26][27] …”

Section: Sample Preparationmentioning

confidence: 99%

Nonextensivity in magnetic nanoparticle ensembles

Binek

Polisetty

et al. 2006

Phys. Rev. B

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A superconducting quantum interference device and Faraday rotation technique are used to study dipolar interacting nanoparticles embedded in a polystyrene matrix. Magnetization isotherms are measured for three cylindrically shaped samples of constant diameter but various heights. Detailed analysis of the isotherms supports Tsallis' conjecture of a magnetic equation of state that involves temperature and magnetic field variables scaled by the logarithm of the number of magnetic nanoparticles. This unusual scaling of thermodynamic variables, which are conventionally considered to be intensive, originates from the nonextensivity of the Gibbs free energy in three-dimensional dipolar interacting particle ensembles. Our experimental evidence for nonextensivity is based on the data collapse of various isotherms that require scaling of the field variable in accordance with Tsallis' equation of state.

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Crossover from extensive to nonextensive behavior driven by long-range interactions

Cited by 103 publications

References 30 publications

Thermostatistics of extensive and non-extensive systems using generalized entropies

Thermostatistics of extensive and non-extensive systems using generalized entropies

Long-range interactions and nonextensivity in ferromagnetic spin models

Nonextensivity in magnetic nanoparticle ensembles

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