Effective lagrangian for the two-dimensional RP2 model at low temperatures

Recent Monte Carlo simulations for the two-dimensional RPN-1 models have shown that the matrix non-linear sigma models (NLσM) have a long-distance behavior which is different from that for the corresponding vector models (SN-1). This discrepancy cannot be explained by the renormalization group (RG) applied to the naive continuum lagrangians (O(N)-(vector NLσ) model). Motivated by this fact, we study the low-temperature long-distance effective lagrangian for the two-dimensional RP2 model by means of the saddle-point (SP) plus renormalization methods. Introducing a matrix order parameter Q via the Hubbard-Stratonovich transformation we analyze the system of a macroscopic effective continuum theory for the Q-field. After taking the O(1)xO(2)-invariant SP for the potential we renormalize the massive fluctuations suppressed by the cut-off. This procedure allows us to find, in addition to the O(3)-model, a new term for the massless modes. Thanks to the new term, it is expected that the infrared RG behavior for the RP2 model could be distinguished from the S2 model. The effective lagrangian itself turns out to be perturbatively non-renormalizable. The RG analysis is formulated in the space of general O(2)-invariant non-linear lagrangians with an infinite number of coupling constants. The first-order RG analysis using the same field-renormalization constant as of the O(3)-model suggests that at long distances the effective lagrangian in the vicinity of zero temperature deviates from the O(3)-model. (orig.)