For the 1D spin-1/2 Heisenberg model with ferromagnetic nearest-neighbor interaction and antiferromagnetic next-nearest neighbor one we present the phase diagram at T = 0 as obtained by DMRG analysis. The interplay of interactions generates two massless and two massive phases in the range of parameters considered. We discuss the properties of the correlations in these phases.

Journal of Physics Conference SeriesJan 1, 20095 citations

Complex-temperature phase diagrams of one-dimensional spin models with next-nearest-neighbor couplings

Robert E. Shrock, Shan-Ho Tsai

arXiv:cond-mat/9703187Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMay 1, 19977 citations

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Phase Diagram of the 1D t-J Model

A. Moreno, A. Muramatsu, Salvatore R. Manmana

Published Jan 1, 2012• 0 citations

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DOI: 10.1007/978-3-642-23869-7_13

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Complex-temperature phase diagrams of one-dimensional spin models with next-nearest-neighbor couplings

Robert E. Shrock, Shan-Ho Tsai

We study the dependence of complex-temperature phase diagrams on details of the Hamiltonian, focusing on the effect of non-nearest-neighbor spin-spin couplings. For this purpose, we consider a simple exactly solvable model, the one-dimensional (1D) Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings. We work out the exact phase diagrams for various values of ${\mathrm{J}}_{\mathrm{NNN}}$ / ${\mathrm{J}}_{\mathrm{NN}}$ and compare these with the case of pure NN couplings. We also give some similar results for the 1D Potts model with NN and NNN couplings.We study the dependence of complex-temperature phase diagrams on details of the Hamiltonian, focusing on the effect of non-nearest-neighbor spin-spin couplings. For this purpose, we consider a simple exactly solvable model, the one-dimensional (1D) Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings. We work out the exact phase diagrams for various values of ${\mathrm{J}}_{\mathrm{NNN}}$/${\mathrm{J}}_{\mathrm{NN}}$ and compare these with the case of pure NN couplings. We also give some similar results for the 1D Potts model with NN and NNN couplings.

arXiv:cond-mat/9703187Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMay 1, 19977 citations

{\mathrm{J}}_{\mathrm{NNN}}

{\mathrm{J}}_{\mathrm{NN}}

and compare these with the case of pure NN couplings. We also give some similar results for the 1D Potts model with NN and NNN couplings.