The Ising model in a random magnetic field h is studied on a square lattice. h has the same value along a row, but varies randomly from row to row. h=\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty} with probability p/2 and is zero with probability 1-p. The quenched free energy F and specific heat C are calculated exactly. We find C\ensuremath{\sim}lnp for small p at the Onsager temperature ${T}_{c}$ . It is shown that for p\ensuremath{\ne}0, F(p,T) is not analytic in T at T= ${T}_{c}$ , i.e., it has a Griffiths-like singularity.The Ising model in a random magnetic field h is studied on a square lattice. h has the same value along a row, but varies randomly from row to row. h=\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty} with probability p/2 and is zero with probability 1-p. The quenched free energy F and specific heat C are calculated exactly. We find C\ensuremath{\sim}lnp for small p at the Onsager temperature ${T}_{c}$. It is shown that for p\ensuremath{\ne}0, F(p,T) is not analytic in T at T=${T}_{c}$, i.e., it has a Griffiths-like singularity.

Physical review. B, Condensed matterMay 1, 19854 citations

Ising Model in a Magnetic Field

Gesualdo Delfino A, Giuseppe Mussardo

NATO ASI series. Series B : PhysicsJan 1, 19970 citations

Random-bond Ising chain in a magnetic field

Julio F. Fernández

The magnetization $m$ as a function of magnetic field $h$ for various temperatures is numerically obtained for the one-dimensional random-bond Ising model with each bond energy either $+J$ or $\ensuremath{-}J$ with equal probability. For high temperatures ( $\frac{\mathrm{kT}}{J}>~0.6$ ) the results obtained agree with those of Landau and Blume. We have obtained $m$ vs $h$ for low temperatures as a numerical approach to the zero-temperature limit.The magnetization $m$ as a function of magnetic field $h$ for various temperatures is numerically obtained for the one-dimensional random-bond Ising model with each bond energy either $+J$ or $\ensuremath{-}J$ with equal probability. For high temperatures ($\frac{\mathrm{kT}}{J}>~0.6$) the results obtained agree with those of Landau and Blume. We have obtained $m$ vs $h$ for low temperatures as a numerical approach to the zero-temperature limit.

Physical review. B, Solid stateDec 1, 197717 citations

One‐dimensional disordered magnetic Ising systems: A new approach

V. Gasparian, David Badalian, Esther Jódar

Abstract We reconsider the problem of a one‐dimensional Ising model with an arbitrary nearest‐neighbor random exchange integral, temperature, and random magnetic field in each site. A convenient formalism is developed that reduces the partition function to a recurrence equation, which is convenient both for numerical as well as for analytical approaches. We have calculated asymptotic expressions for an ensemble averaged free energy and the averaged magnetization in the case of strong and weak couplings in external constant magnetic field. With a random magnetic field at each site in addition to nearest‐neighbor random exchange integrals we also evaluated the free energy. We show that the zeros of the partition function for the Ising model in the complex external magnetic field plane formally coincide with the singularities of the real part of electron's transmission amplitude through the chain of δ‐function potentials.Abstract We reconsider the problem of a one‐dimensional Ising model with an arbitrary nearest‐neighbor random exchange integral, temperature, and random magnetic field in each site. A convenient formalism is developed that reduces the partition function to a recurrence equation, which is convenient both for numerical as well as for analytical approaches. We have calculated asymptotic expressions for an ensemble averaged free energy and the averaged magnetization in the case of strong and weak couplings in external constant magnetic field. With a random magnetic field at each site in addition to nearest‐neighbor random exchange integrals we also evaluated the free energy. We show that the zeros of the partition function for the Ising model in the complex external magnetic field plane formally coincide with the singularities of the real part of electron's transmission amplitude through the chain of δ‐function potentials.

physica status solidi (b)Jul 7, 20090 citations

{T}_{c}

. It is shown that for p\ensuremath{\ne}0, F(p,T) is not analytic in T at T=

{T}_{c}

, i.e., it has a Griffiths-like singularity.

The magnetization

m

as a function of magnetic field

h

for various temperatures is numerically obtained for the one-dimensional random-bond Ising model with each bond energy either

+J

or $\ensuremath{-}J$ with equal probability. For high temperatures (

\frac{\mathrm{kT}}{J}>~0.6

) the results obtained agree with those of Landau and Blume. We have obtained

m

h

for low temperatures as a numerical approach to the zero-temperature limit.