Abstract
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 L x . We find that finitesize corrections to scaling are of the form $a_k/L^{2k1}_x$ for the free energy f and $b_k(p)/L_x^{2k1}$ and $c_k(p)/L_x^{2k1}$ for inverse correlation lengths $\xi^{1}_p$ and $\xi^{1}_{Lp}$ , respectively, with integer values of k. By exact evaluation we find that the amplitude ratios $b_k(p)/a_k$ and $c_k(p)/a_k$ are universal and verify this universal behavior using a perturbative conformal approach.
Original language  English 

Journal  EPL 
Volume  111 
Issue number  6 
DOIs  
Publication status  Published  12 Oct 2015 
Fingerprint
Dive into the research topics of 'The critical Ising model on a torus with a defect line'. Together they form a unique fingerprint.Profiles

Ralph Kenna
 Research Centre for Fluid and Complex Systems  Professor of Theoretical Physics
Person: Teaching and Research