The low-temperature phase of Kac-Ising models

We analyse the low temperature phase of ferromagnetic Kac-Ising models in dimensions $d\geq 2$. We show that if the range of interactions is \g^{-1}, then two disjoint translation invariant Gibbs states exist, if the inverse temperature \b satisfies \b -1\geq \g^\k where \k=\frac {d(1-\e)}{(2d+1)(d+1)}, for any \e>0. The prove involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous spin system which is suitable for the use of a variant of the Peierls argument.Comment: 19pp, Plain Te

Study of the work roll cooling in hot rolling process with regard on service life

Operational conditions and many studies confirmed that the work rolls cooling in hot rolling process havesignificant impact on damage and service life. The specific approach based on the numerical simulation andexperimental results of the work roll cooling optimization and service life improvement is presented in this paper.The 3D finite element model was prepared for the numerical simulations of the work roll cooling. The FE modelrepresents circular sector of the work roll. The model is fully parametric. It is capable to simulate a roll with anydiameter, any thickness. Each of the model parameters can be easily changed based on user requirements. Thestress state is calculated by ANSYS in two steps. At first, the thermal conditions as starting temperature of the roll,cooling intensity and so on are applied and time dependent thermal analysis is performed. The temperature fieldof work roll is obtained from transient thermal analysis and is used as thermal loads in second step. In the secondstep structural analysis is carried out. The other relevant boundary conditions as normal, shear and contactpressure are considered in structural analysis. The Tselikov load distribution model is used for normal and shearstress distribution in a rolling gap. The boundary conditions for FE analysis are prepared in software MATLAB. Allconsidered boundary conditions are based on real measured data from hot rolling mills.The results of the performed analyses are focused on the description of the assessing methodology of the workrolls cooling on the stresses, deformations and service life of the rolls

Entropy-driven phase transition in a polydisperse hard-rods lattice system

We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals

General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions that admit convergent contour expansions. We derive formulas for the positions and the density of the zeros. In particular, we show that for models without symmetry, the curves on which the zeros lie are generically not circles, and can have topologically nontrivial features, such as bifurcation. Our results are illustrated in three models in a complex field: the low-temperature Ising and Blume-Capel models, and the $q$-state Potts model for $q$ large enough.Comment: 4 pgs, 2 figs, to appear in Phys. Rev. Let

SURFACE INDUCED FINITE-SIZE EFFECTS FOR FIRST ORDER PHASE TRANSITIONS

We consider classical lattice models describing first-order phase transitions, and study the finite-size scaling of the magnetization and susceptibility. In order to model the effects of an actual surface in systems like small magnetic clusters, we consider models with free boundary conditions. For a field driven transition with two coexisting phases at the infinite volume transition point $h=h_t$, we prove that the low temperature finite volume magnetization m_{\free}(L,h) per site in a cubic volume of size $L^d$ behaves like m_\free(L,h)=\frac{m_++m_-}2 + \frac{m_+-m_-}2 \tanh \bigl(\frac{m_+-m_-}2\,L^d\, (h-h_\chi(L))\bigr)+O(1/L), where $h_\chi(L)$ is the position of the maximum of the (finite volume) susceptibility and $m_\pm$ are the infinite volume magnetizations at $h=h_t+0$ and $h=h_t-0$, respectively. We show that $h_\chi(L)$ is shifted by an amount proportional to $1/L$ with respect to the infinite volume transitions point $h_t$ provided the surface free energies of the two phases at the transition point are different. This should be compared with the shift for periodic boun\- dary conditons, which for an asymmetric transition with two coexisting phases is proportional only to $1/L^{2d}$. One also consider the position $h_U(L)$ of the maximum of the so called Binder cummulant U_\free(L,h). While it is again shifted by an amount proportional to $1/L$ with respect to the infinite volume transition point $h_t$, its shift with respect to $h_\chi(L)$ is of the much smaller order $1/L^{2d}$. We give explicit formulas for the proportionality factors, and show that, in the leading $1/L^{2d}$ term, the relative shift is the same as that for periodic boundary conditions.Comment: 65 pages, amstex, 1 PostScript figur

Mean-field driven first-order phase transitions in systems with long-range interactions

We consider a class of spin systems on $\Z^d$ with vector valued spins (\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions $d\ge3$, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions $d=1,2$ for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique ``state,'' then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.Comment: 57 pages; uses a (modified) jstatphys class fil

Band structure of CuMnAs probed by optical and photoemission spectroscopy

The tetragonal phase of CuMnAs progressively appears as one of the key materials for antiferromagnetic spintronics due to efficient current-induced spin-torques whose existence can be directly inferred from crystal symmetry. Theoretical understanding of spintronic phenomena in this material, however, relies on the detailed knowledge of electronic structure (band structure and corresponding wave functions) which has so far been tested only to a limited extent. We show that AC permittivity (obtained from ellipsometry) and UV photoelectron spectra agree with density functional calculations. Together with the x-ray diffraction and precession electron diffraction tomography, our analysis confirms recent theoretical claim [Phys. Rev. B 96, 094406 (2017)] that copper atoms occupy lattice positions in the basal plane of the tetragonal unit cell