Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics C Solid State Physics

Frustrated Ising chains. III

B G S Doman

Published Sep 30, 1982• 4 citations
Publisher

Abstract

For pt.II see ibid., vol.15, p.1693 (1982). The methods developed by Williams (1981) to describe the ground-state properties of a random-bond infinite Ising chain are extended to apply to a system of finite-length random-bond Ising chains. It is shown how to evaluate the magnetisation, ground-state energy, and entropy as a function of magnetic field. It is shown that the steps in the magnetisation and entropy when B=2J/r behave differently for r even and r odd. The magnetisation and entropy remain finite as B becomes very small.

DOI
10.1088/0022-3719/15/27/020

Related papers

Low-temperature properties of frustrated Ising chains

B G S Doman, John Kino Yamaguchi Williams

Recently published methods used to examine the ground-state properties of the random-bond Ising chain in a uniform magnetic field are extended to describe the system at low temperatures. The entropy spikes broaden asymmetrically, and the excitation energy and specific heat become asymmetric double-peaked functions of the magnetic field with zero values between the peaks at B=2J/r for integer r. The magnetisation steps at B=2J/r are smoothed out asymmetrically. Both the ground-state and finite-temperature properties of a simple periodic frustrated Ising chain are investigated using the transfer-matrix method. The ground-state properties are similar to those of the random bond chain; the ground-state entropy, for instance, is finite for J<or=B<or=2J, with spikes at J and 2J.

Journal of Physics C Solid State Physics•Mar 20, 1982•7 citations

Ground State Properties of Frustrated Ferromagnetic Ising Chains in a Uniform-Random-External Magnetic Field.

Dr.MANSOOR Dr.MANSOOR, A-Z. HABEEB

The methods of Williams,Doman and Williams,and Doman and Habeeb are used to describe the ground state properties of infinite ferromagnetic Ising chains in a random field.Analytic results for the ground state energy,the magnetisation per spin in the direction of the local field and the entropy as a function of magnetic field are obtained. When the probability factor of the zero local field is zero,our results are in agreement with thut obtained previously by Williams. terminators.A terminator could be defined as the simplest group of spins whose direction is indepen- dent of that of its neighbours,but depends on the value of the magnetic field.The behaviour of the system is now dominated by these subchains and so we take into account all possible configurations for such subchains.The idea of superspins and superb- onds introduced by Williams(1981)and applied later to examine the properties of many Ising

Journal of Engineering Research (Libya)•Jun 30, 1995•0 citations

Ground state properties of frustrated Ising chains

John Kino Yamaguchi Williams

The ground state properties of several frustrated chains are investigated in a simple physically transparent manner. The ground state energy, magnetisation, nearest-neighbour correlations and zero-point entropy are evaluated by considering explicitly the flipping of well defined spin clusters at certain critical field strengths.

Journal of Physics C Solid State Physics•Oct 10, 1981•16 citations

Ising Chains Properties at Low Temperature Extended Analysis

Mansoor A.Z. Habeeb, Nazera Khalil Dakhil, Fatimah O. Salman

The transfer matrix method is used to describe the properties of the random bond of a simple periodic frustrated Ising chain in a uniform magnetic field. Doman and Williams(1982) are found expressions for the thermodynamic functions of the system at low temperature. Their methods is extended to apply to a system of five-antiferromagnetic bond Ising chain terminated by a ferromagnetic bond at low temperatures. New expressions for the magnetization, energy, and entropy as a functions of magnetic field is found. All results are in agreement with the previous results.

Journal of Kufa for Mathematics and Computer•Dec 1, 2014•0 citations

Random-bond Ising chain in a magnetic field at low temperatures

Alexander Vilenkin

The low-temperature behavior ($T\ensuremath{\ll}h, J$) of a random-bond Ising chain in a magnetic field is considered [$H=\ensuremath{-}(\frac{1}{2})J\ensuremath{\Sigma}{T}_{i}{\ensuremath{\sigma}}_{i}{\ensuremath{\sigma}}_{i+1}\ensuremath{-}h\ensuremath{\Sigma}{\ensuremath{\sigma}}_{i}, {\ensuremath{\sigma}}_{i}=\ifmmode\pm\else\textpm\fi{}1$, ${{T}_{i}}$ is a fixed random sequence of numbers +1 and -1 with concentrations ${c}_{1}$ and ${c}_{2}=1\ensuremath{-}{c}_{1}$, respectively]. The ground-state energy ${E}_{0}$, magnetization ${\ensuremath{\mu}}_{0}$ and zero-point entropy ${S}_{0}$ are calculated exactly. It is shown that ${\ensuremath{\mu}}_{0}$ and ${S}_{0}$ are discontinuous functions of magnetic field having jumps at $h=\frac{J}{n}$, $n=1, 2, \dots{}$.

Physical review. B, Condensed matter•Aug 1, 1978•26 citations

The ground state for Ising model ±J on the tube

M. Błaszyk

Abstract The Ising model with exchange integrals ±J for a square lattice spanned over infinite length tubes of the width of 2, 3, or 4 bonds is considered. The paper gives a short description of a method of linear equations allowing a reduction of a physical problem of determination of e.g. energy, entropy, magnetisation for systems with frozen disorder, to a solution of a system of linear equations. The results for energy, entropy and magnetisation possible for a short presentation are given.

physica status solidi (b)•Mar 1, 2003•1 citation
For pt.II see ibid., vol.15, p.1693 (1982). The methods developed by Williams (1981) to describe the ground-state properties of a random-bond infinite Ising chain are extended to apply to a system of finite-length random-bond Ising chains. It is shown how to evaluate the magnetisation, ground-state energy, and entropy as a function of magnetic field. It is shown that the steps in the magnetisation and entropy when B=2J/r behave differently for r even and r odd. The magnetisation and entropy remain finite as B becomes very small.
Recently published methods used to examine the ground-state properties of the random-bond Ising chain in a uniform magnetic field are extended to describe the system at low temperatures. The entropy spikes broaden asymmetrically, and the excitation energy and specific heat become asymmetric double-peaked functions of the magnetic field with zero values between the peaks at B=2J/r for integer r. The magnetisation steps at B=2J/r are smoothed out asymmetrically. Both the ground-state and finite-temperature properties of a simple periodic frustrated Ising chain are investigated using the transfer-matrix method. The ground-state properties are similar to those of the random bond chain; the ground-state entropy, for instance, is finite for J<or=B<or=2J, with spikes at J and 2J.
The methods of Williams,Doman and Williams,and Doman and Habeeb are used to describe the ground state properties of infinite ferromagnetic Ising chains in a random field.Analytic results for the ground state energy,the magnetisation per spin in the direction of the local field and the entropy as a function of magnetic field are obtained. When the probability factor of the zero local field is zero,our results are in agreement with thut obtained previously by Williams. terminators.A terminator could be defined as the simplest group of spins whose direction is indepen- dent of that of its neighbours,but depends on the value of the magnetic field.The behaviour of the system is now dominated by these subchains and so we take into account all possible configurations for such subchains.The idea of superspins and superb- onds introduced by Williams(1981)and applied later to examine the properties of many Ising
The transfer matrix method is used to describe the properties of the random bond of a simple periodic frustrated Ising chain in a uniform magnetic field. Doman and Williams(1982) are found expressions for the thermodynamic functions of the system at low temperature. Their methods is extended to apply to a system of five-antiferromagnetic bond Ising chain terminated by a ferromagnetic bond at low temperatures. New expressions for the magnetization, energy, and entropy as a functions of magnetic field is found. All results are in agreement with the previous results.
The low-temperature behavior ($T\ensuremath{\ll}h, J$) of a random-bond Ising chain in a magnetic field is considered [$H=\ensuremath{-}(\frac{1}{2})J\ensuremath{\Sigma}{T}_{i}{\ensuremath{\sigma}}_{i}{\ensuremath{\sigma}}_{i+1}\ensuremath{-}h\ensuremath{\Sigma}{\ensuremath{\sigma}}_{i}, {\ensuremath{\sigma}}_{i}=\ifmmode\pm\else\textpm\fi{}1$, Ti{{T}_{i}}Ti​ is a fixed random sequence of numbers +1 and -1 with concentrations c1{c}_{1}c1​ and ${c}_{2}=1\ensuremath{-}{c}_{1}$, respectively]. The ground-state energy E0{E}_{0}E0​, magnetization ${\ensuremath{\mu}}_{0}$ and zero-point entropy S0{S}_{0}S0​ are calculated exactly. It is shown that ${\ensuremath{\mu}}_{0}$ and S0{S}_{0}S0​ are discontinuous functions of magnetic field having jumps at h=Jnh=\frac{J}{n}h=nJ​, n=1,2,…n=1, 2, \dots{}n=1,2,….