Commentaries.- A Survey by the Editors.- I. Thermodynamic Limit for Coulomb Systems.- I. 1 Existence of Thermodynamics for Real Matter with Coulomb Forces.- I. 2 The Constitution of Matter: Existence of Thermodynamics for Systems Composed of Electrons and Nuclei.- II. Hard Sphere Virial Coefficients.- II. 1 Suppression at High Temperature of Effects Due to Statistics in the Second Virial Coefficient of a Real Gas.- II. 2 Calculation of Exchange Second Virial Coefficient of a Hard-Sphere Gas by Path Integrals.- III. Zeros of Partition Functions.- III. 1 Monomers and Dimers.- III. 2 Theory of Monomer-Dimer Systems.- III. 3 A Property of Zeros of the Partition Function for Ising Spin Systems.- III. 4 A General Lee-Yang Theorem for One-Component and Multicomponent Ferromagnets.- IV. Reflection Positivity.- IV. 1 Existence of Phase Transitions for Anisotropic Heisenberg Models.- IV. 2 Phase Transitions in Anisotropic Lattice Spin Systems.- IV. 3 Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions.- IV. 4 Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models.- IV. 5 Phase Transitions and Reflection Positivity. II. Lattice Systems with Short-Range and Coulomb Interactions.- IV. 6 Lattice Models for Liquid Crystals.- IV. 7 Existence of Neel Order in Some Spin-1/2 Heisenberg Antiferromagnets.- IV. 8 The XY Model Has Long-Range Order for all Spins and all Dimensions Greater than One.- V. Classical Thermodynamics.- V. 1 The Third Law of Thermodynamics and the Degeneracy of the Ground State for Lattice Systems.- V. 2 A Guide to Entropy and the Second Law of Thermodynamics.- V. 3 A Fresh Look at Entropy and the Second Law of Thermodynamics.- VI. Lattice Systems.- VI. 1 Properties of a Harmonic Crystal in a Stationary Nonequilibrium State.- VI. 2 The Statistical Mechanics of Anharmonic Lattices.- VI. 3 Time Evolution of Infinite Anharmonic Systems.- VI. 4 Lattice Systems with a Continuous Symmetry III. Low Temperature Asymptotic Expansion for the Plane Rotator Model.- VII. Miscellaneous.- VII. 1 The Finite Group Velocity of Quantum Spin Systems.- VII. 2 The Classical Limit of Quantum Spin Systems.- VII. 3 A Refinement of Simon's Correlation Inequality.- VII. 4 Fluxes, Laplacians, and Kasteleyn's Theorem.- Selecta of Elliott H. Lieb.- Publications of Elliott H. Lieb.Commentaries.- A Survey by the Editors.- I. Thermodynamic Limit for Coulomb Systems.- I. 1 Existence of Thermodynamics for Real Matter with Coulomb Forces.- I. 2 The Constitution of Matter: Existence of Thermodynamics for Systems Composed of Electrons and Nuclei.- II. Hard Sphere Virial Coefficients.- II. 1 Suppression at High Temperature of Effects Due to Statistics in the Second Virial Coefficient of a Real Gas.- II. 2 Calculation of Exchange Second Virial Coefficient of a Hard-Sphere Gas by Path Integrals.- III. Zeros of Partition Functions.- III. 1 Monomers and Dimers.- III. 2 Theory of Monomer-Dimer Systems.- III. 3 A Property of Zeros of the Partition Function for Ising Spin Systems.- III. 4 A General Lee-Yang Theorem for One-Component and Multicomponent Ferromagnets.- IV. Reflection Positivity.- IV. 1 Existence of Phase Transitions for Anisotropic Heisenberg Models.- IV. 2 Phase Transitions in Anisotropic Lattice Spin Systems.- IV. 3 Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions.- IV. 4 Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models.- IV. 5 Phase Transitions and Reflection Positivity. II. Lattice Systems with Short-Range and Coulomb Interactions.- IV. 6 Lattice Models for Liquid Crystals.- IV. 7 Existence of Neel Order in Some Spin-1/2 Heisenberg Antiferromagnets.- IV. 8 The XY Model Has Long-Range Order for all Spins and all Dimensions Greater than One.- V. Classical Thermodynamics.- V. 1 The Third Law of Thermodynamics and the Degeneracy of the Ground State for Lattice Systems.- V. 2 A Guide to Entropy and the Second Law of Thermodynamics.- V. 3 A Fresh Look at Entropy and the Second Law of Thermodynamics.- VI. Lattice Systems.- VI. 1 Properties of a Harmonic Crystal in a Stationary Nonequilibrium State.- VI. 2 The Statistical Mechanics of Anharmonic Lattices.- VI. 3 Time Evolution of Infinite Anharmonic Systems.- VI. 4 Lattice Systems with a Continuous Symmetry III. Low Temperature Asymptotic Expansion for the Plane Rotator Model.- VII. Miscellaneous.- VII. 1 The Finite Group Velocity of Quantum Spin Systems.- VII. 2 The Classical Limit of Quantum Spin Systems.- VII. 3 A Refinement of Simon's Correlation Inequality.- VII. 4 Fluxes, Laplacians, and Kasteleyn's Theorem.- Selecta of Elliott H. Lieb.- Publications of Elliott H. Lieb.

Nov 29, 200411 citations

Phase Transitions in Anisotropic Lattice Spin Systems

Jürg Martin Fröhlich, Élliott H. Lieb

Springer eBooksJan 1, 1978129 citations

Spin-liquid and spin-glass behavior in quantum spin models with all-to-all p -spin interactions

Shusei Wadashima, Yukitoshi Motome

Spin-liquid and spin-glass states represent two distinct phases of disordered quantum spin systems. These states are, in principle, distinguished by quantum-entangled fluctuations and spin freezing, but identifying each state and characterizing the transition between them remains challenging. Here, we systematically explore the relationship between the spin-liquid and spin-glass states using a model with all-to-all random interactions among $p$ spins, which interpolates between the Ising-like one-component, XY-like two-component, and isotropic three-component cases. By analyzing the system-size $N$ dependence of the Edwards-Anderson order parameter and the density of states, we identify the transition from the spin liquid to the spin glass for various values of $p$ . We show that the phase diagrams for different $p$ can be unified through a scaling with $N/{p}^{2}$ , revealing that increasing anisotropy in the interactions systematically suppresses the spin-liquid phase and extends the spin-glass regime. Furthermore, we examine the competition between multiple-spin interactions and anisotropy under an external magnetic field in the isotropic case, and find that the spin-liquid phase transitions into the spin-glass phase before entering a quantum paramagnetic phase. Our findings provide insights into quantum disordered phases and the transitions between them.Spin-liquid and spin-glass states represent two distinct phases of disordered quantum spin systems. These states are, in principle, distinguished by quantum-entangled fluctuations and spin freezing, but identifying each state and characterizing the transition between them remains challenging. Here, we systematically explore the relationship between the spin-liquid and spin-glass states using a model with all-to-all random interactions among $p$ spins, which interpolates between the Ising-like one-component, XY-like two-component, and isotropic three-component cases. By analyzing the system-size $N$ dependence of the Edwards-Anderson order parameter and the density of states, we identify the transition from the spin liquid to the spin glass for various values of $p$. We show that the phase diagrams for different $p$ can be unified through a scaling with $N/{p}^{2}$, revealing that increasing anisotropy in the interactions systematically suppresses the spin-liquid phase and extends the spin-glass regime. Furthermore, we examine the competition between multiple-spin interactions and anisotropy under an external magnetic field in the isotropic case, and find that the spin-liquid phase transitions into the spin-glass phase before entering a quantum paramagnetic phase. Our findings provide insights into quantum disordered phases and the transitions between them.

arXiv:2508.08154Physical review. B./Physical review. BNov 4, 20250 citations

Phase transitions in anisotropic lattice spin systems

Jürg Martin Fröhlich, Élliott H. Lieb

Communications in Mathematical PhysicsOct 1, 1978128 citations

Stability and decay rates of nonisotropic attractive Bose-Einstein condensates

Cristián Huepe, Laurette S. Tuckerman, Stéphane Métens +1 more

Nonisotropic attractive Bose-Einstein condensates are investigated numerically with Newton and inverse Arnoldi methods. The stationary solutions of the Gross-Pitaevskii equation and their linear stability are computed. Bifurcation diagrams are calculated and used to find the condensate decay rates corresponding to macroscopic quantum tunneling, two-three-body inelastic collisions, and thermally induced collapse. Isotropic and nonisotropic condensates are compared. The effect of anisotropy on the bifurcation diagram and the decay rates is discussed. Spontaneous isotropization of the condensates is found to occur. The influence of isotropization on the decay rates is characterized near the critical point.Nonisotropic attractive Bose-Einstein condensates are investigated numerically with Newton and inverse Arnoldi methods. The stationary solutions of the Gross-Pitaevskii equation and their linear stability are computed. Bifurcation diagrams are calculated and used to find the condensate decay rates corresponding to macroscopic quantum tunneling, two-three-body inelastic collisions, and thermally induced collapse. Isotropic and nonisotropic condensates are compared. The effect of anisotropy on the bifurcation diagram and the decay rates is discussed. Spontaneous isotropization of the condensates is found to occur. The influence of isotropization on the decay rates is characterized near the critical point.

arXiv:cond-mat/0212069Physical Review AAug 27, 200346 citations

p

spins, which interpolates between the Ising-like one-component, XY-like two-component, and isotropic three-component cases. By analyzing the system-size

N

dependence of the Edwards-Anderson order parameter and the density of states, we identify the transition from the spin liquid to the spin glass for various values of

p

. We show that the phase diagrams for different

p

can be unified through a scaling with

N/{p}^{2}

, revealing that increasing anisotropy in the interactions systematically suppresses the spin-liquid phase and extends the spin-glass regime. Furthermore, we examine the competition between multiple-spin interactions and anisotropy under an external magnetic field in the isotropic case, and find that the spin-liquid phase transitions into the spin-glass phase before entering a quantum paramagnetic phase. Our findings provide insights into quantum disordered phases and the transitions between them.