  An equilibrium random surface multistep height model proposed in [Abraham and
Newman, EPL, 86, 16002 (2009)] is studied using a variant of the worm
algorithm. In one limit, the model reduces to the two-dimensional Ising model
in the height representation. When the Ising model constraint of single height
steps is relaxed, the critical temperature and critical exponents are
continuously varying functions of the parameter controlling height steps larger
than one. Numerical estimates of the critical exponents can be mapped via a
single parameter-- the Coulomb gas coupling-- to the exponents of the O(n) loop
model on the honeycomb lattice with n <= 1.
