scholarly journals Long-range vector models at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Noam Chai ◽  
Mikhail Goykhman ◽  
Ritam Sinha
Keyword(s):  
Long Range ◽  
Short Range ◽  
Conformal Symmetry ◽  
Vector Model ◽  
Entire Region ◽  
Crossover Point ◽  
Range Interaction ◽  
Large N ◽  
Long Range Interaction ◽  
Range Vector

Abstract We calculate various CFT data for the O(N) vector model with the long-range interaction, working at the next-to-leading order in the 1/N expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point s* of the exponent parameter s. We also develop the N > 1 generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region d/2 < s < s*.

SHORT-TIME DYNAMICS OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2003 ◽  
Vol 17 (23) ◽  
pp. 1227-1236 ◽  
Author(s):  
YUAN CHEN ◽  
ZHI-BING LI
Keyword(s):  
Long Range ◽  
High Temperature Phase ◽  
Vector Model ◽  
Temperature Phase ◽  
Range Interaction ◽  
Time Dynamics ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Short Time ◽  
N Vector

The short-time critical behavior of the random n-vector model with long-range interaction is studied by the theoretic renormalization-group approach. After a sudden quench to the critical temperature from the high temperature phase, the system is released to an evolution within model A dynamics. The initial slip exponents and the dynamic exponent are calculated to two-loop order.

THE AGING BEHAVIOR OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2007 ◽  
Vol 21 (23) ◽  
pp. 1555-1568 ◽  
Author(s):  
YUAN CHEN
Keyword(s):  
Long Range ◽  
Vector Model ◽  
Aging Behavior ◽  
Range Interaction ◽  
Fluctuation Dissipation ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Long Time ◽  
Short Time ◽  
N Vector

The aging behavior of the random n-vector model with long-range interaction decaying as r-(d+σ) (where d is the dimensionality), is investigated by the theoretic renormalization-group approach. The system initially disordered at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with model A dynamics. The aging properties are studied by the short-time expansions. The scaling behavior of two-time response and correlation functions are obtained in a frame of the expansion in ∊ = 2σ-d. In dimensions d < 2σ, the long-time limit of the critical fluctuation dissipation ratio X∞ is calculated up to one-loop order. The simulation of X∞ is discussed.

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.

PECULIARITIES OF ORDERING DUE TO DISORDER IN PLANAR ANTIFERROMAGNETIC DEGENERATE STRUCTURES

1997 ◽  
Vol 04 (01) ◽  
pp. 9-14
Author(s):  
V. M. ROZENBAUM
Keyword(s):  
Long Range ◽  
Short Range ◽  
Dipole Moments ◽  
Range Order ◽  
Square Lattice ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Long Range Interaction ◽  
2D System ◽  
Ground State Degeneracy

A model is suggested which allows a description of low-temperature behavior for a 2D system of dipole moments on a square lattice with an arbitrary anisotropic long-range interaction giving rise to continuously degenerate antiferromagnetic ground states. It is shown that the breaking of the ground-state degeneracy and intersublattice ordering of dipole moments caused by thermodynamic fluctuations are responsible for long-range-order initiation in systems with anisotropic interaction and for short-range-order conservation in systems with isotropic short-range interaction.

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.

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