Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.

https://iopscience.iop.org/article/10.1088/0305-4470/39/22/R01/pdf

Rare region effects at classical, quantum and nonequilibrium phase transitions

Charge- and spin-density waves in existing superconductors: competition between Cooper pairing and Peierls or excitonic instabilities

Calorimetric Investigation of Phase Transitions Occurring in Molecule-Based Magnets†

The magnetic properties of SrCu2 (BO3)2 are reviewed from a theoretical point of view. SrCu2 (BO3)2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu2 (BO3)2. In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu2 (BO3)2. The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.

https://iopscience.iop.org/article/10.1088/0953-8984/15/9/201/pdf

Theory of the orthogonal dimer Heisenberg spin model for SrCu2 (BO3)2

In a previous paper a possibility of coexistence of two superconducting order parameters was discussed for the (1, 1, 0) surface of d x 2 - y 2 -wave superconductors. In the present report physical properties are examined particularly for the time-reversal-breaking state ( s ± i d ) near the (1, 1, 0) surface. The nature of coexisting order parameters shows up in the local density of states. It is also shown that the superconducting current flows along the surface due to the time reversal breaking and induces the magnetic field. The induced magnetic field can be used to detect the time-reversal-breaking states experimentally.

Coexistence of Different Symmetry Order Parameters near a Surface in d-Wave Superconductors III

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Approximate Method for the Free Energy

The magnetization process in the Shastry-Sutherland system is studied by using the third-order perturbation expansion. It is shown that the 1/3-plateau is realized by the second-order perturbation, which is not prevented by the off-diagonal part. In each subspace whose magnetization per dimer is less than 1/3, the lowest energy state is determined by a small but finite energy-gain due to the third-order correlated flip terms and there exists no plateau originating from the third-order effect. Our results are compared with those of the exact diagonalization method to discuss the validity of truncation of states in our perturbation theory.

Magnetization Process in the Shastry-Sutherland System SrCu2(BO3)2. Results of Third-Order Dimer Expansion.

The uniform susceptibility and triplet excitation spectrum of the Heisenberg antiferromagnet on the one-fifth depleted square lattice are calculated using the third-order perturbation expansion method from the viewpoint of the weakly coupled meta-plaquette picture. Both the susceptibility and triplet excitation spectrum data for CaV 4 O 9 are simultaneously explained. The origin of the relatively large spin gap in this compound is discussed.

Susceptibility and triplet excitation spectrum for CaV4O9 : Third-order perturbation expansions

Variational Theory of the Heisenberg Ferromagnet

The extended Hubbard model with nearest-neighbor (NN) Coulomb repulsion is used to study superconductivity in a static charge-density-wave (CDW) state. It is found that the doped carriers form a large Fermi surface and are condensed into the ${d}_{\mathrm{xy}}$-wave superconducting state from the $\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2}$ CDW state stabilized by the NN Coulomb repulsion. The superconductivity coexisting with a CDW order observed in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ [S. Kr\"amer and M. Mehring, Phys. Rev. Lett. 83, 396 (1999)] together with the superconductivity of ${\mathrm{Pr}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4\ensuremath{-}y}$ [M. Brinkmann, H. Bach, and K. Westerholt, Physica C 292, 104 (1997)] may be important examples of this pairing mechanism.

Akihide Oguchi

Papers

Approximate Method for the Free Energy

Magnetization Process in the Shastry-Sutherland System SrCu2(BO3)2. Results of Third-Order Dimer Expansion.

Susceptibility and triplet excitation spectrum for CaV4O9 : Third-order perturbation expansions

Variational Theory of the Heisenberg Ferromagnet

d-wave pairing in the doped static charge-density-wave state on a two-dimensional square lattice