A. Basuev. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Zusammenfassung
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.
%0 Book Section
%1 statphys23_0790
%A Basuev, A.G.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K contour equation equations ising layering many-phase model state statphys23 surface topic-1 transitions
%T Ising Model in Half-space. Layering Transitions
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=790
%X 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.
@incollection{statphys23_0790,
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 $\mathbb{C}^{\Phi
},\Phi$ -- 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
$\mathbb{C}^{\Phi}.$
For Ising model in half-space with small values
of temperature and mixing boundary condition it is proven for each
external field $\mu $ 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 $\mu $ in points $\mu _{q}$ the
thickness $q(\mu )$ changes stepwise with unit magnitude and $q(\mu
)\rightarrow\infty$ when $\mu\rightarrow +0.$ 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 $\mu _{0}$ in the zero-layer, the
external field outside the zero-layer $\mu >0.$ 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.},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Basuev, A.G.},
biburl = {https://www.bibsonomy.org/bibtex/2df1dff1488ad4d7559c6ad7c659fe239/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {46d1dbbfd1019d3ab95faccdafc388be},
intrahash = {df1dff1488ad4d7559c6ad7c659fe239},
keywords = {contour equation equations ising layering many-phase model state statphys23 surface topic-1 transitions},
month = {9-13 July},
timestamp = {2007-06-20T10:16:29.000+0200},
title = {Ising Model in Half-space. Layering Transitions},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=790},
year = 2007
}