arXiv subjects
Publications and source records attributed to E. S. Pisanova.
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.
A $d$--dimensional quantum model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_τ^{z}$ ($L$--linear space size and $L_τ$--temporal size) and subjected to periodic boundary conditions is considered. Because of its close relation with the quantum rotors model it can be regarded as an effective model for studying the low-temperature behavior of the quantum Heisenberg antiferromagnets. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0\leq d^{\prime}\leq d$ a detailed analysis, in terms of the special functions of classical mathematics, for the free energy, the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.