# Asymptotics and thermodynamics of spin-pattern formation probability in equilibrium spin systems

- Authors
- Journal
- Physics Letters A 0375-9601
- Publisher
- Elsevier
- Publication Date
- Volume
- 301
- Identifiers
- DOI: 10.1016/s0375-9601(02)01080-0
- Disciplines

## Abstract

Abstract A general formula for the asymptotic form of any spin-pattern formation probability is given in equilibrium spin systems. This yields thermodynamics of the emptiness formation probability P( n) in spin chains. In particular, P( n) is shown to take the asymptotic form P( n)∼exp[ n( f− e s)/ k B T] in the anisotropic XXZ spin chain. Here, f is the free energy per site and e s is the energy eigenvalue per site for a completely ferromagnetic state, namely e s=− J z − μ B H for the z– z exchange interaction J z and an external magnetic field H. A new formulation to calculate P( n) explicitly for any n is also given, and the above asymptotic form has been confirmed thereby in the Ising chain and in the isotropic XY-model (in which J z =0).

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