Premium
Short‐Time Behaviour of the Transverse Auto‐Correlation Function of the 1D XY‐Model
Author(s) -
Farias G. A.,
Gonçalves L. L.
Publication year - 1987
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221390131
Subject(s) - correlation function (quantum field theory) , limit (mathematics) , transverse field , physics , classical xy model , constant (computer programming) , transverse plane , function (biology) , correlation , field (mathematics) , chain (unit) , convergence (economics) , statistical physics , mathematical analysis , mathematics , condensed matter physics , quantum mechanics , geometry , pure mathematics , phase transition , computer science , dielectric , ising model , economic growth , structural engineering , engineering , biology , evolutionary biology , programming language , economics
Abstract The dynamics of the spin 1/2 one‐dimensional XY‐model in a transverse field is considered. The short‐time behaviour of the auto‐correlation function 〈 S j x ( t ) S j x (0)〉 for the closed chain is obtained numerically by considering the exact results known for the open chain which are given in terms of Pfaffians. The bulk auto‐correlation is identified with the correlation 〈 S 20 x ( t ) S 20 x (0)〉 for the open chain, and this identification is shown to be valid up to a characteristic time Jt ≅ 20. It is also shown, as expected, that the boundary effects are more pronounced for fields smaller than the exchange constant ( h < | J |) and in the low temperature limit. The results are obtained for different temperatures and field strengths, and the numerical convergence is discussed in each case.