Residual entropy of the dilute Ising chain in a magnetic field

Abstract

The properties of the ground state of the simplest frustrated system, the dilute Ising chain in a magnetic field, are rigorously investigated over the entire range of concentrations of charged non-magnetic impurities. Analytical methods are proposed for calculating the residual entropy of frustrated states, including states at phase boundaries, which are based on the Markov property of the system and involve solving a linear optimization problem for energy and a nonlinear optimization problem for entropy. These methods allow obvious generalizations for one-dimensional pseudospin models with anisotropic interactions. We calculate the composition, entropy and magnetization for the ground state phases. We prove the absence of pseudo-transitions in the dilute Ising chain, since the residual entropy of states at phase boundaries is always higher than the entropy of adjacent phases. The concentration dependencies of magnetization at the phase boundaries are obtained, and unlike linear dependencies for adjacent phases, they have nonlinear behavior. Field-induced transitions between ground states and entropy jumps associated with them are also considered, and in particular, it is shown that the field-induced transition from an antiferromagnetic state to a frustrated one is accompanied by charge ordering.

arXiv comment10 pages, 3 figures, 3 tables

References in corpus (35)

• Enhanced magnetocaloric effect in frustrated magnets
• Magnetocaloric effect in one-dimensional antiferromagnets
• Magnetocaloric effect in pyrochlore antiferromagnet Gd2Ti2O7
• Thermal entanglement in exactly solvable Ising-XXZ diamond chain structure
• Dynamic and thermodynamic properties of the generalised diamond chain model for azurite
• Pairwise thermal entanglement in Ising-XYZ diamond chain structure in an external magnetic field
• Vigorous thermal excitations in a double-tetrahedral chain of localized Ising spins and mobile electrons mimic a temperature-driven first-order phase transition
• Exactly solvable Ising--Heisenberg chain with triangular XXZ-Heisenberg plaquettes
• Spin frustration of a spin-1/2 Ising-Heisenberg three-leg tube as an indispensable ground for thermal entanglement
• Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions
• Thermal Entanglement of a Spin-1/2 Ising-Heisenberg Model on a Symmetrical Diamond Chain
• Magnetization process, bipartite entanglement and enhanced magnetocaloric effect of the exactly solved spin-1/2 Ising-Heisenberg tetrahedral chain
• Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter-leg couplings
• Universality and quasicritical exponents of one-dimensional models displaying a quasitransition at finite temperatures
• Magnetization non-rational quasi-plateau and spatially modulated spin order in the model of the single-chain magnet, [{(CuL)_2 Dy}{Mo(CN)_8}] 2CH_3CN H_2O
• Magnetic properties of the spin-1/2 Ising-Heisenberg diamond chain with the four-spin interaction
• Zero temperature non-plateau magnetization and magnetocaloric effect in an Ising-XYZ diamond chain structure
• Correlation functions for a spin-$\frac{1}{2}$ Ising-XYZ diamond chain: Further evidence for quasi-phases and pseudo-transitions
• Spin frustration and fermionic entanglement in an exactly solved hybrid diamond chain with the localized Ising spins and mobile electrons
• Towards low-temperature peculiarities of thermodynamic quantities for decorated spin chains
• Geometrical frustration of an extended Hubbard diamond chain in the quasi-atomic limit
• Quantum entanglement in the neighborhood of pseudo-transition for a spin-1/2 Ising-XYZ diamond chain
• Magnetic Gruneisen parameter and magnetocaloric properties of a coupled spin-electron double-tetrahedral chain
• Heterobimetallic Dy-Cu coordination compound as a classical-quantum ferrimagnetic chain of regularly alternating Ising and Heisenberg spins
• Exactly solved mixed spin-(1,1/2) Ising-Heisenberg distorted diamond chain
• Unconventional low temperature features in the one-dimensional frustrated $q$-state Potts model
• Modified strong-coupling treatment of a spin-1/2 Heisenberg trimerized chain developed from the exactly solved Ising-Heisenberg diamond chain
• Macroscopic ground-state degeneracy and magnetocaloric effect in the exactly solvable spin-1/2 Ising-Heisenberg double-tetrahedral chain
• Low temperature pseudo-phase transition in an extended Hubbard diamond chain
• Frustrated diamond-chain quantum $XXZ$ Heisenberg antiferromagnet in a magnetic field
• Effective low-energy description of almost Ising-Heisenberg diamond chain
• Unusual field-induced transitions in exactly solved mixed spin-(1/2,1) Ising chain with axial and rhombic zero-field splitting parameters
• Local distributions of the 1D dilute Ising model
• Thermodynamic features of the 1D dilute Ising model in the external magnetic field
• Exactly solvable spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins

Cited by in corpus (5)

• Pseudotransitions in a dilute Ising chain
• Zero temperature phase transitions and their anomalous influence on thermodynamic behavior in the q-state Potts model on a diamond chain
• Spectral mechanism and nearly reducible transfer matrices for pseudotransitions in one-dimensional systems
• Residual Entropy of Ice: A Study Based on Transfer Matrices
• Correlation functions and properties of local distributions of frustrated phases in the ground state of a dilute Ising chain in a magnetic field