O(3) model with Nienhuis action

Understand

We study the O(3) sigma model in $D=2$ on the lattice with a Boltzmann weight linearized in $\beta$ on each link.

• While the spin formulation now suffers from a sign-problem the equivalent loop model remains positive and becomes particularly simple.
• By studying the transfer matrix and by performing Monte Carlo simulations in the loop form we study the mass gap coupling in a step scaling analysis.
• The question addressed is, whether or not such a simplified action still has the right universal continuum limit.