Application of the linear filtering algorithm to two models with non-trivial topology

✍ Scribed by S. Amir-Azizi; G.J. Daniell

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 503 KB
• Volume: 70
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(92)90106-9

✦ Synopsis

We extend the linear filtering method of Monte Carlo simulation, introduced in a previous paper, to two models where the quadratic approximation to the action does not hold. The first model considered is the quantum anharmonic oscillator with the double well potential V=(x 2 -x~)2on a time lattice of spacing ~t. Using a modified potential V', where e_V'~ĩ s a sum of two Gaussian peaks, leads to the introduction of spin variables labelling the two wells in addition to continuous variables representing fluctuations around the minima. The configurations can be generated recursively and the method proves substantially quicker than the Metropolis simulation of the model. The second model considered is the two-dimensional periodic Gaussian model, were addition formulae for the Jacobi theta functions allow the recursive generation of configurations. It is possible to obtain reliable estimates of correlation functions at high temperatures.