Finite size and temperature effects in the $J_1-J_2$ model on a strip

Within Takahashi's spin-wave theory we study finite size and temperature effects near the quantum critical point in the $J_{1}-J_{2}$ Heisenberg antiferromagnet defined on a strip ($L\times\infty$). In the continuum limit, the theory predicts universal finite size and temperature corrections and describes the dimensional crossover in magnetic properties from 2+1 to 1+1 space-time dimensions.