scholarly journals Quantum and classical criticalities in the frustrated two-leg Heisenberg ladder

2008 ◽  
Vol 86 (4) ◽  
pp. 509-513 ◽  
Author(s):  
M Azzouz ◽  
B Ramakko
Keyword(s):  
Heisenberg Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Exchange Interactions ◽  
Thermal Fluctuations ◽  
Temperature Dependences ◽  
Wigner Transformation ◽  
75.10 Jm ◽  
75.50 Ee ◽  
Antiferromagnetic Heisenberg Model

This paper is about the frustration-induced criticality in the antiferromagnetic Heisenberg model on the two-leg ladder with exchange interactions along the chains, rungs, and diagonals, and also about the effect of thermal fluctuations on this criticality. The method used is the bond-mean-field theory, which is based on the Jordan–Wigner transformation in dimensions higher than one. In this paper, we will summarize the main results presented in a talk, and report on new results about the couplings and temperature dependences of the spin susceptibility.PACS Nos.: 75.10.Jm, 75.10.Dg, 75.50.Ee

Spontaneous magnetization of ferromagnet in mean-field Heisenberg model

2019 ◽  
Vol 33 (04) ◽  
pp. 1950036 ◽  
Author(s):  
Artur P. Durajski ◽  
Anna B. Olesik ◽  
Anita E. Auguscik
Keyword(s):  
Field Theory ◽  
Magnetic Susceptibility ◽  
Curie Temperature ◽  
Heisenberg Model ◽  
Spontaneous Magnetization ◽  
Mean Field Theory ◽  
Mean Field ◽  
Function Technique ◽  
Heisenberg Ferromagnet ◽  
Temperature Dependences

The Heisenberg ferromagnet model has been studied theoretically using the Weiss mean-field theory and Green’s function technique. The equations for the Curie temperature, magnetization, and magnetic susceptibility were analytically derived. Moreover, we proved, that our results are useful in description of real materials. The calculated value of Curie temperature for [Formula: see text] alloy correspond well with the experimental results obtained recently on the base of the temperature dependences of magnetization.

scholarly journals Interplay between field-induced and frustration-induced quantum criticalities in the frustrated two-leg Heisenberg ladder

2008 ◽  
Vol 86 (9) ◽  
pp. 1125-1132 ◽  
Author(s):  
B Ramakko ◽  
M Azzouz
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
External Magnetic Field ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Susceptibility ◽  
The Other ◽  
Wigner Transformation ◽  
75.10 Jm ◽  
Physical Quantities

The antiferromagnetic Heisenberg two-leg ladder in the presence of frustration and an external magnetic field is a system that is characterized by two sorts of quantum criticalities, not only one. One criticality is the consequence of intrinsic frustration, and the other one is a result of the external magnetic field. So the behaviour of each of them in the presence of the other deserves to be studied. Using the Jordan–Wigner transformation in dimensions higher than one and the bond-mean-field theory we examine the interplay between the field-induced and frustration-induced quantum criticalities in this system. The present work could constitute a prototype for those systems showing multiple, perhaps sometimes competing, quantum criticalities. We calculate several physical quantities such as magnetization and spin susceptibility as functions of field and temperature.PACS Nos.: 75.10.Jm 73.43.Nq 75.10.Pq 75.10.Dg

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