The critical Ising model on a torus with a defect line
1 Yerevan Physics Institute - Alikhanian Brothers 2, 375036 Yerevan, Armenia
2 Applied Mathematics Research Centre, Coventry University - Coventry, UK
Received: 16 July 2015
Accepted: 21 September 2015
The critical Ising model in two dimensions with a specific defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically the partition function and the asymptotic expansions of the free energy and inverse correlation lengths for an infinitely long cylinder of circumference Lx. We find that finite-size corrections to scaling are of the form for the free energy f and and for inverse correlation lengths and , respectively, with integer values of k. By exact evaluation we find that the amplitude ratios and are universal and verify this universal behavior using a perturbative conformal approach.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 75.10.-b – General theory and models of magnetic ordering
© EPLA, 2015