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Wu X.,Beijing Normal University | Izmailyan N.,Coventry University | Izmailyan N.,Ai Alikhanyan National Science Laboratory
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

The critical two-dimensional Ising model is studied with four types boundary conditions: free, fixed ferromagnetic, fixed antiferromagnetic, and fixed double antiferromagnetic. Using bond propagation algorithms with surface fields, we obtain the free energy, internal energy, and specific heat numerically on square lattices with a square shape and various combinations of the four types of boundary conditions. The calculations are carried out on the square lattices with size N×N and 30

Izmailian N.S.,Beijing Normal University | Izmailian N.S.,Ai Alikhanyan National Science Laboratory
Journal of Physics A: Mathematical and Theoretical | Year: 2012

We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑ ∞p = 0fp(, k)S -p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio eff = /sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation eff → 1/eff. This article is part of 'Lattice models and integrability', a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday. © 2012 IOP Publishing Ltd.

Karyan G.,Ai Alikhanyan National Science Laboratory
Physics of Particles and Nuclei | Year: 2014

The HERMES collaboration has measured charge-separated pion and kaon multiplicities in semi-inclusive deep inelastic scattering using a 27.6 GeV electron or positron beam scattering off a hydrogen or deuterium target. The results are presented as a function of the Bjorken variable xB, the negative squared four-momentum transfer Q 2, the hadron fractional energy z and it's transverse momentum Ph ⊥. These data will be very useful to understand the quark-fragmentation process in deep-inelastic hadron electro-production and will serve as crucial input in the understanding of spin asymmetries in polarized semi-inclusive deep-inelastic scattering. © 2014 Pleiades Publishing, Ltd.

Wu X.,Beijing Normal University | Zheng R.,Beijing Normal University | Izmailian N.,Coventry University | Izmailian N.,Ai Alikhanyan National Science Laboratory | Guo W.,Beijing Normal University
Journal of Statistical Physics | Year: 2014

The bond-propagation algorithm for the specific heat of the two dimensional Ising model is developed and that for the internal energy is completed. Using these algorithms, we study the critical internal energy and specific heat of the model on the square lattice and triangular lattice with free boundaries. Comparing with previous works (Phys Rev E 86:041149, 2012; Phys Rev E 87:022124, 2013), we reach much higher accuracy (10-28) of the internal energy and specific heat, compared to the accuracy 10-11 of the internal energy and 10-9 of the specific heat reached in the previous works. This leads to much more accurate estimations of the edge and corner terms. The exact values of all edge and corner terms are therefore conjectured. The accurate forms of finite-size scaling for the internal energy and specific heat are determined for the rectangle-shaped square lattice with various aspect ratios and various shaped triangular lattice. For the rectangle-shaped square and triangular lattices and the triangle-shaped triangular lattice, there is no logarithmic correction terms of order higher than 1/S, with S the area of the system. For the triangular lattice in rhombus, trapezoid and hexagonal shapes, there exist logarithmic correction terms of order higher than 1/S for the internal energy, and logarithmic correction terms of all orders for the specific heat. © 2014 Springer Science+Business Media New York.

Rojas O.,Federal University of Lavras | Rojas M.,Federal University of Lavras | Ananikian N.S.,Ai Alikhanyan National Science Laboratory | De Souza S.M.,Federal University of Lavras
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2012

Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial- interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field, and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature. © 2012 American Physical Society.

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