Abstract. We investigate the tricritical Ising model in complex magnetic field in order to characterize the analytic structure of its free energy. By supplementing analytic methods with the truncation of conformal space technique we obtain nonperturbative data even if the field theories we consider are not integrable. The existence of edge singularities analogous to the Yang–Lee points in the Ising field theory is confirmed. A surprising result, due to the conformal dimensions of the operators involved, is the appearance of two branching points which seems appealing to identify with a pair of complex conjugate spinodal singularities.
We investigate the tricritical Ising model in a complex magnetic field in order to characterize the analytic structure of its free energy. By supplementing analytic methods with the truncation of conformal space technique we obtain non-perturbative data even if the field theories that we consider are not integrable. The existence of edge singularities analogous to the Yang–Lee points in the Ising field theory is confirmed. A surprising result, due to the conformal dimensions of the operators involved, is the appearance of two branching points which it seems appealing to identify with a pair of complex conjugate spinodal singularities.
The analytic properties of the Onsager solution of the two-dimensional Ising lattice in zero external magnetic field are investigated. The free energy above the critical temperature
Tc can be regarded as an analytic function in the
u plane, where $u=\mathrm{exp}(\ensuremath{-}\frac{4J}{{k}_{B}T})$, with singularities at $u=0, \ensuremath{\infty}, \mathrm{and} \mathrm{exp}(\ifmmode\pm\else\textpm\fi{}\frac{4J}{{k}_{B}{T}_{c}})$. But its analytic continuation below the critical temperature does not describe a stable thermodynamic phase. Similar statements are true for the free energy below the critical temperature. The famous logarithmic singularity is briefly discussed. Finally, the knowledge of the analytic properties is shown, by elementary considerations, to explain the nonanalytic behavior at vanishing external field below the critical temperature---a result first enunciated by Yang and Lee for the free energy in the presence of an external magnetic field.