Abstract
The extension of Pirogov-Sinai theory is developed. Results
applicable for bulk and surface phases of lattice models are proved,
and state equation is constructed. The region of first-order phase
transition is extended in external fields space to $C^\Phi
,\Phi$ -- the phase set of a model. It is proved the next extension
of Lee-Yang theorem: the partition functions with stable
boundary condition have no zeros in external fields space
$C^\Phi.$
For Ising model in half-space with small values
of temperature and mixing boundary condition it is proven for each
external field $$ the existence of the spin layer with the
thickness $q(\mu)$ over the bottom boundary. In this layer the average of
spin is approximately -1 and outside one is about +1. With the
decreasing of the external field $$ in points $_q$ the
thickness $q()$ changes stepwise with unit magnitude and $q(\mu
)\rightarrowınfty$ when $\mu+0.$ In points $\mu_q$
there is the coexistence of two surface phases. The free surface
energy is proven the piecewise analytical function in region
Re $\mu>0$ and small values of temperature. It is considered also the model with
the external arbitrary field $_0$ in the zero-layer, the
external field outside the zero-layer $>0.$ In the latter case
the phase diagram of layering transitions is also constructed (see figure 1, outside ABCD). The Antonov's rule is proved. Using the surface state equation the points $B_0$ and $B_1$ of coexistence phases $\0,1,2\$ and $\0,2,3\$ with the accuracy
of $x^7,x=\exp(-2\varepsilon)$ are constructed.
Users
Please
log in to take part in the discussion (add own reviews or comments).