Linear and Nonlinear Responses and Universality of Critical Exponents in Hamiltonian Systems with Long-Range Interaction

2017 ◽  
Author(s):  
Shun Ogawa ◽  
Yoshiyuki Y. Yamaguchi
Keyword(s):  
Long Range ◽  
Hamiltonian Systems ◽  
Critical Exponents ◽  
Range Interaction ◽  
Nonlinear Responses ◽  
Long Range Interaction ◽  
Linear And Nonlinear

scholarly journals Critical Behaviour in Systems in which Long-Range and Short-Range Forces Compete

2019 ◽  
pp. 37-47 ◽  
Author(s):  
S.V. Belim
Keyword(s):  
Critical Exponent ◽  
Long Range ◽  
Critical Exponents ◽  
Short Range ◽  
Asymptotic Series ◽  
Critical Behaviour ◽  
Interaction Parameters ◽  
Theory Approach ◽  
Range Interaction ◽  
Long Range Interaction

Critical behaviour of a range of ferromagnetic materials deviates from the predictions of the Ising, XY and Heisenberg models. Additional long-range forces competing with regular exchange interaction may explain this deviation. These competing interactions lead to new universality classes of critical behaviour. The paper uses the field theory approach to investigate critical behaviour in those systems in which long-range and short-range forces compete. We consider the case when a power function of distance r-D-σ, when 1.5 < σ < 2.0, can describe the long-range forces. There exists a distinctive critical behaviour mode for these values. We derived vertex functions using a two-loop approximation directly in three-dimensional space (D = 3) and, for all values, obtained a linear approximation of asymptotic series in terms of long-range interaction parameters. We applied the Pade --- Borel summation technique to these asymptotic series. We computed stable fixed points and critical exponents as functions of long-range interaction parameters for low relativeefficiency of the long-range interaction. We investigated how critical exponents depend on the factor in the power law and relative long-range interaction intensity. We compared our results to the critical exponent values found experimentally for manganites. We used the experimental critical exponent γ values to compute long-range interaction parameters and then used the long-range interaction parameters to derive the ß exponent values, which we then compared to the experimental values. We show good agreement between our theoretical results and experimental data.

Phase transformation and Raman spectra in BaTiO3 nanocrystals

2002 ◽  
Vol 718 ◽  
Author(s):  
Jian Yu ◽  
X. J. Meng ◽  
J.L. Sun ◽  
G.S. Wang ◽  
J.H. Chu
Keyword(s):  
Particle Size ◽  
Phase Transformation ◽  
Low Temperature ◽  
Long Range ◽  
Lattice Expansion ◽  
Inversion Symmetry ◽  
Range Interaction ◽  
Cooperative Phenomena ◽  
Long Range Interaction ◽  
Hydrothermal Methods

AbstractIn this paper, size-induced ferroelectricit yweakening, phase transformation, and anomalous lattice expansion are observed in nanocrystalline BaTiO3 (nc-BaTiO3) deriv ed b y low temperature hydrothermal methods, and they are w ellunderstood using the terms of the long-range interaction and its cooperative phenomena altered by particle size in covalen t ionic nanocrystals. In cubic nc-BaTiO3, five modes centerd at 186, 254, 308, 512 and 716 cm-1 are observed Raman active in cubic nanophase, and they are attributed to local rhombohedral distortion breaking inversion-symmetry in cubic nanophase. The254 and 308 cm-1 modes are significantly affected not only by the concentration of hydroxyl defects, but also their particular configuration. And the 806 cm-1 modes found to be closely associated with OH - absorbed on grain boundaries.

scholarly journals Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1624
Author(s):  
Leonid Litinskii ◽  
Boris Kryzhanovsky
Keyword(s):  
Inverse Problem ◽  
Long Range ◽  
Random Number ◽  
Connection Matrix ◽  
Range Interaction ◽  
Connection Matrices ◽  
Ising Systems ◽  
Long Range Interaction ◽  
Matrix Spectrum ◽  
Analytical Expressions

In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of its eigenvalues. In addition, we define restrictions allowing a random number sequence to be a connection matrix spectrum. We use the previously obtained analytical expressions for the eigenvalues of Ising connection matrices accounting for an arbitrary long-range interaction and supposing periodic boundary conditions.

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