# Poster presented by Brian J. Pendleton

**Poster Session**
**Topic:** Algorithms and Machines

**Authors:** A D Kennedy and B J Pendleton

### Cost of Generalised HMC Algorithms for Free Field Theory

**Abstract:** We study analytically the computational cost the Generalised Hybrid Monte Carlo algorithm. We show how to calculate the autocorrelation functions of polynomial operators of arbitrary degree in the fields. For linear and quadratic operators we optimise the GHMC momentum mixing angle, the trajectory length, and the integration stepsize. We show explicitly that long trajectories are optimal, and that standard HMC is much more efficient than algorithms based on the Second Order Langevin / Kramers Equation. We show that, contrary to naive expectations, HMC and L2MC/KE have the same volume dependence, but their dynamical citical exponents are z = 1 and z= 3/2 respectively.

Massimo Campostrini,
`campo@mailbox.difi.unipi.it`