Summary: Among the models of interacting classical statistical mechanics the Yang-Baxter (YB) integrable systems play a special role [R. J. Baxter, Exactly solved models in statistical mechanics. London-New York etc.: Academic Press. A Subsidiary of Harcourt Brace Jovanovich, Publishers (1982; Zbl 0538.60093)]. The central model in the theory of YB integrable systems is the six vertex model. The model under our consideration is the Izergin-Korepin (IK) nineteen vertex model, which can be viewed as a generalization of the six vertex model [A. G. Izergin and V. E. Korepin, The inverse scattering method approach to the quantum Shabat-Mikhailov model. Prepr. LOMI E-3–80 (1980; Zbl 0441.35053)].