Quantum Monte-Carlo study of phase transitions in Heisenberg chains with long-range interactions

Ordering transitions in the Heisenberg ferromagnetic chains are studied using the Handscomb quantum Monte-Carlo method. The spin-coupling parameter depends as r(-p) on the distance r between spins. The spin correlation function, susceptibility and long-range order are investigated. The transition is found to exist when p < 2 in agreement with previous predictions. Temperatures of the transition and critical exponents are estimated. No indications of the transition are found when p greater than or equal to 2. In the case of p = 2 (the Haldane-Shastry model) the Monte-Carlo results agree with known exact formulae. (C) 2001 Elsevier Science B.V. All rights reserved.