Multicritical Crossovers near the Dilute Bose Gas Quantum Critical Point

Many zero temperature transitions, involving the deviation in the value of a U(1) conserved charge from a quantized value, are described by the dilute Bose gas quantum critical point. On such transitions, we study the consequences of perturbations which break the symmetry down to $Z_N$ in $d$ spatial dimensions. For the case $d=1\mathrm{}$, $N=2\mathrm{}$, we obtain exact, finite temperature, multicritical crossover functions by a mapping to an integrable lattice model.