Lattice Systems with a Continuous Symmetry III . Low Temperature Asymptotic Expansion for the Plane Rotator Model
نویسندگان
چکیده
We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d = 3.
منابع مشابه
Lattice Systems with a Continuous Symmetry I. Perturbation Theory for Unbounded Spins
We investigate a continuous Ising system on a lattice, equivalently an anharmonic crystal, with interactions: Σ (Φx~Φy) 2 + λ(φx-φy)\ 0 x eR, xeTL . <*,y> We prove that the perturbation expansion for the free energy and for the correlation functions is asymptotic about /L = 0, despite the fact that the reference system (/l = 0) does not cluster exponentially. The results can be extended to more...
متن کاملExternal and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method
The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...
متن کاملVII.B Topological Defects in the XY model
As stated in the previous section, thermal excitation of Goldstone modes destroys spontaneous order in two dimensional models with a broken continuous symmetry. The RG study of the non-linear σ-model confirms that the transition temperature of n-component spins vanishes as T ∗ = 2πǫ/(n− 2) for ǫ = (d− 2) → 0. However, the same RG procedure appears to suggest a different behavior for n = 2. The ...
متن کاملVII.B Topological Defects in the XY model
As stated in the previous section, thermal excitation of Goldstone modes destroys spontaneous order in two dimensional models with a broken continuous symmetry. The RG study of the non-linear σ-model confirms that the transition temperature of n-component spins vanishes as T ∗ = 2πǫ/(n − 2) for ǫ = (d − 2) → 0. However, the same RG procedure appears to suggest a different behavior for n = 2. Th...
متن کاملLow-temperature asymptotics of integrable systems in an external field
An asymptotic low-temperature expansion is performed for an integrable bosonic lattice model and for the critical spin-1/2 Heisenberg chain in a magnetic field. The results apply to the integrable Bose gas as well. We also comment on a high-temperature expansion of the bosonic lattice model. PACS numbers: 02.30Ik, 05.30.-d, 05.30.Jp, 75.10.Pq
متن کامل