Abstract
By using self-dual clusters (whose sizes are characterized by the numbers $b=2,3,4,5$), we calculate within a real-space renormalization-group framework, the longitudinal surface tension of the square-lattice first-neighbor \textonehalf{}-spin ferromagnetic Ising model. The exact critical temperature ${T}_{c}$ is recovered for any value of $b$; the exact asymptotic behavior of the surface tension in the limit of low temperatures is analytically recovered; the approximate correlation-length critical exponents monotonically tend towards the exact value $\ensuremath{\nu}=1$ (which, for two dimensions, coincides with the surface-tension critical exponent $\ensuremath{\mu}$) for increasingly large cells; the same behavior is noticed in the approximate values for the surface-tension amplitude in the limit $T\ensuremath{\rightarrow}{T}_{c}$. We develop four different numerical procedures for extrapolating to $b\ensuremath{\rightarrow}\ensuremath{\infty}$ the renormalization-group (RG) results for the surface tension, and quite satisfactory agreement is obtained with Onsager's exact expression (error varying from zero to a few percent on the whole temperature domain). Furthermore, we compare the set of RG surface tensions with a set of biased surface tensions (associated with appropriate misfit seams) and find only fortuitous coincidence among them.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.