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Thermodynamics of a one-dimensional frustrated spin- 1 2 Heisenberg ferromagnet

2008; American Physical Society; Volume: 78; Issue: 17 Linguagem: Inglês

10.1103/physrevb.78.174412

1550-235X

M. Härtel, Johannes Richter, D. Ihle, S.‐L. Drechsler,

Physics of Superconductivity and Magnetism

We calculate the thermodynamic quantities (correlation functions $⟨{\mathbf{S}}_{0}{\mathbf{S}}_{n}⟩$, correlation length $\ensuremath{\xi}$, spin susceptibility $\ensuremath{\chi}$, and specific heat ${C}_{V}$) of the frustrated one-dimensional spin-half ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg ferromagnet, i.e., for ${J}_{2}<0.25|{J}_{1}|$, using a rotation-invariant Green's-function formalism and full diagonalization of finite lattices. We find that the critical indices are not changed by ${J}_{2}$, i.e., $\ensuremath{\chi}={y}_{0}{T}^{\ensuremath{-}2}$ and $\ensuremath{\xi}={x}_{0}{T}^{\ensuremath{-}1}$ at $T\ensuremath{\rightarrow}0$. However, the coefficients ${y}_{0}$ and ${x}_{0}$ linearly decrease with increasing ${J}_{2}$ according to the relations ${y}_{0}=(1\ensuremath{-}4{J}_{2}/|{J}_{1}|)/24$ and ${x}_{0}=(1\ensuremath{-}4{J}_{2}/|{J}_{1}|)/4$, i.e., both coefficients vanish at ${J}_{2}=0.25|{J}_{1}|$ indicating the zero-temperature phase transition that is accompanied by a change in the low-temperature behavior of $\ensuremath{\chi}$ $(\ensuremath{\xi})$ from $\ensuremath{\chi}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ $(\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}1})$ at ${J}_{2}<0.25|{J}_{1}|$ to $\ensuremath{\chi}\ensuremath{\propto}{T}^{\ensuremath{-}3/2}$ $(\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}1/2})$ at ${J}_{2}=0.25|{J}_{1}|$. In addition, we detect the existence of an additional low-temperature maximum in the specific heat when approaching the critical point at ${J}_{2}=0.25|{J}_{1}|$.