Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations

Journal Article · Sat Jul 01 04:00:00 EDT 1995 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02178358· OSTI ID:468299

Kawashima, N; Gubernatis, J E ^[1]

---

1. Los Alamos National Lab., NM (United States)

We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition function of quantum spin models with an arbitrary spin magnitude in arbitrary dimensions. This generalized representation enables us to develop a new cluster algorithm for the simulation of quantum spin systems by the worldline Monte Carlo method. Because the Swendsen-Wang algorithm is based on the FK representation, the new cluster algorithm naturally includes it as a special case. As well as the general description of the new representation, we present an illustration of our new algorithm for some special interesting cases: the Ising model, the antiferromagnetic Heisenberg model with S=1, and a general Heisenberg model. The new algorithm is applicable to models with any range of the exchange interaction, any lattice geometry, and any dimensions.

• Sponsoring Organization: USDOE
• OSTI ID: 468299
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 80; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
HEISENBERG MODEL
ISING MODEL
MONTE CARLO METHOD
PARTITION FUNCTIONS
SIMULATION
SPIN
W CODES