Ising models with long-range dipolar and short-range ferromagnetic interactions

Details Ising models with long-range dipolar and short-range ferromagnetic interactions Ising models with long-range dipolar and short-range ferromagnetic interactions

2006-04-28

arxiv.org/abs/cond-mat/0604668v2

Physics

Condensed Matter

Statistical Mechanics

16 pages; references added, minor changes in the introduction and one remark added after theorem 3. Final version, to appear i

Scientific paper

10.1103/PhysRevB.74.064420

We study the ground state of a $d$--dimensional Ising model with both long range (dipole--like) and nearest neighbor ferromagnetic (FM) interactions. The long range interaction is equal to $r^{-p}$, $p>d$, while the FM interaction has strength $J$. If $p>d+1$ and $J$ is large enough the ground state is FM, while if $d1$ the ground state has a series of transitions from an antiferromagnetic state of period 2 to $2h$--periodic states of blocks of sizes $h$ with alternating sign, the size $h$ growing when the FM interaction strength $J$ is increased (a generalization of this result to the case $0

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