Size effects in finite systems with long-range interactions

E. S. LOSCAR; C. M. HOROWITZ

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2018 vol. 97 p. 32103 - 32103

1539-3755

Small systems consisting of particles interacting with long-range potentials exhibit enormous size effects.The Tsallis conjecture [C. Tsallis, Fractals  {f 3}, 541 (1995)], valid fortranslationally invariant systems with long-range interactions, states a well-known scaling relating different sizes. Here, we propose to generalize this conjecture to systems with this symmetry broken, by adjusting one parameter that determines an effective distance to compute the strength of the interaction. We apply this proposal to the one-dimensional Ising Model with ferromagnetic interactions that decay as $1/r^{1+sigma}$ in the region where the model has a finite critical temperature. We demonstrate the convenience of using this generalization to study finite-size effects, and we compare this approach withthe finite-size scaling theory.