Embedded dynamics for ${\mathrm{\phi }}^4$ theory

A new Monte Carlo dynamics is proposed for ${\mathrm{\phi }}^4$ field theory that reduces critical slowing down. Discrete Ising variables are embedded into the field theory, so that large-scale tunneling events can be induced via a modified Swendsen-Wang algorithm with fluctuating site-bond percolation probabilities. The measured dynamical critical exponents ${\mathrm{z}}_{\mathrm{EL}=0.07\mathrm{}\pm }$0.07, 0.29±0.09, and 0.87±0.20 in one, two, and three dimensions, respectively, are consistent with our conjecture that this embedded dynamics lies in the same universality class as the Swendsen-Wang Ising dynamics.