Random Spin Systems Research Articles

Decay to equilibrium in random spin systems on a lattice

We study continuous and discrete spin systems on a lattice with random interactions of finite range. In particular for sufficiently large interactions we prove no spectral gap property in the high temperature region. Moreover we show that in two dimensions, if the temperature is sufficiently high and the probability of interaction to be large is small enough, we have an almost sure stretched exponential upper bound for the decay to equilibrium.

Transport properties of stage-1 graphite intercalation compounds

Stage-1 graphite intercalation compounds approximate quasi-two-dimensional (2D) random spin systems with competing ferromagnetic and antiferromagnetic intraplanar exchange interactions. The temperature dependence of the in-plane electrical resistivity of these compounds has been measured near critical temperatures. The magnetic resistivity consists of the long-range spin-order part and the spin-fluctuation part . For the long-range spin-order part is dominant: the temperature dependence of is described by a smeared power law with an exponent , where is the critical exponent of staggered magnetization. For the spin-fluctuation part becomes larger than . For no appreciable magnetic resistivity is observed. For c = 1 the derivative shows a small peak at around 67 K due to the growth of short-range spin order which is characteristic of the 2D Heisenberg antiferromagnet. The critical behaviour of the in-plane resistivity can be explained in terms of a model based on - d exchange interactions between -electrons in the graphite layers and magnetic spins in the intercalate layers. The -electrons are scattered by spins of a virtual antiferromagnetic in-plane spin configuration arising from the superposition of two ferromagnetic in-plane structures with spin directions antiparallel to each other. The - d exchange interactions of these compounds are also discussed.

Non-frustrated random spin systems with gauge symmetry

We introduce a class of random spin systems without frustration, which satisfies the conditions for gauge symmetry. The method of gauge transformation provides several properties on the phase diagram of gauge symmetric models; this method is almost rigorous, while the derivation for the absence of re-entrance contains unproved assumption. In the present random models, the absence of re-entrance can be shown exactly. Furthermore, the phase diagram and the critical properties are exactly related with those in the original pure system. The present random systems correspond to the Mattis model with asymmetric bond distribution in the Ising case, and a kind of the gauge glass model in the XY case. In the case of the clock model in two dimensions, we find a new thermodynamic phase which has long-range spin-glass correlation with critical (power-decaying) ferromagnetic correlation.

Ground-State Phase Diagram of the Two-Dimensional Quantum Heisenberg Mattis Model

The two-dimensional $S=1/2$ asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The N\'eel order parameter and the spin glass order parameter can be smoothly extrapolated to the thermodynamic limit in the antiferromagnetic region, as in the pure Heisenberg antiferromagnet. The critical concentration of the N\'eel phase is consistent with that of the two-dimensional Ising Mattis model, and the spin glass order parameter increases monotonously as the ferro-bond concentration increases. These facts suggest that quantum fluctuation does not play an essential role in two-dimensional non-frustrated random spin systems. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, N\'eel order, spin glass order

Relaxation Modes in Random Spin Systems

A method of finding slow relaxation modes in random spin systems is proposed. For stochastic dynamics, an approximate relaxation mode { f i } and its relaxation rate λ are determined from an eigenvalue problem ∑ j C i , j ( t 0 + t ) f j =exp (-λ t ) ∑ j C i , j ( t 0 ) f j , where C i , j ( t )=< S i ( t ) · S j (0)> is the correlation matrix of spins. The method is applied to the two-dimensional ± J Ising spin glass below the critical temperature of the corresponding nonrandom ferromagnet. It is found through Monte Carlo simulations that the slow relaxation modes obtained by the present method describe the long-time behavior of spins well. The slow relaxation modes are spatially localized and can be regarded as clusters. The distribution of the relaxation rates is consistent with the prediction of the theory which assumes independent motion of clusters.

Correlation decay in low-dimensional spin glasses

A new method to investigate the two-point correlation function decay in a finite size random spin system and at finite temperatures is proposed. It is applicable to systems with cyclic boundary conditions and in any local or uniform magnetic field. The efficiency of this method is presented in the case of an isotropic XY spin glass model with Gaussian bond distribution in external field. Using unitary U(1) gauge transformation and operator inequalities we have obtained explicit upper bounds for generalized spin-glass susceptibility κ(T,R) that describes off-diagonal transverse magnetization in two dimensional random XY spin lattices at finite temperatures. It is found that the slowest possible decay for susceptibility in random XY spin glass is of the Kosterlitz–Thouless-type with power-law decay in 2D, and the exponential type in 1D, at low temperatures. These upper bounds rule out the possibility of the corresponding magnetic ordering in 1D and 2D isotropic XY spin glasses at finite temperatures.

Strong decay to equilibrium in one-dimensional random spin systems

We consider a spin system on a lattice with finite-range, possibly unbounded random interactions. We show that for such systems the Glauber dynamics cannot decay to equilibrium exponentially fast in L2 even at high temperatures. Additionally, for one-dimensional systems with unbounded random couplings we prove that with probability one the corresponding Glauber dynamics has a fast (subexponential) decay to equilibrium in the uniform norm, provided that the distribution of random couplings satisfies some exponential bound.

Magnetic phase transition of stage-2 CucCo1-cCl2-graphite intercalation compounds.

Stage-2 ${\mathrm{Cu}}_{\mathit{c}}$${\mathrm{Co}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$${\mathrm{Cl}}_{2}$-graphite intercalation compounds (GIC's) (0\ensuremath{\le}c\ensuremath{\le}1) provide ideal two-dimensional random spin systems with a spin frustration effect arising from competing ferromagnetic and antiferromagnetic interactions. The magnetic properties of these compounds have been studied by dc and ac magnetic susceptibility, and superconducting quantum interference device magnetization. The sign of the Curie-Weiss temperature changes from positive to negative with increasing concentration around c=0.80 to 0.85. The intraplanar exchange interaction J(Cu-Co) between ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Co}}^{2+}$ spins is ferromagnetic and depends on the Cu concentration. These systems with c0.9 undergo a ferromagnetic phase transition at the critical temperature ${\mathit{T}}_{\mathit{c}}$. The irreversible effect of magnetization is observed below ${\mathit{T}}_{\mathit{c}}$. The low-temperature phase below ${\mathit{T}}_{\mathit{c}}$ may correspond to a cluster glass phase where the spin direction of ferromagnetic clusters is frozen because of frustrated interisland interactions which include a dipole-dipole interaction and an interplanar antiferromagnetic interaction. The critical temperature ${\mathit{T}}_{\mathit{c}}$ increases as c increases and exhibits a broad maximum around c=0.5. This enhancement of ${\mathit{T}}_{\mathit{c}}$ is partly due to the ferromagnetic interaction J(Cu-Co). No magnetic phase transition is observed for 0.9c1 partly because of the spin frustration effects arising from (i) the competition between ferromagnetic J(Cu-Co) and antiferromagnetic J(Cu-Cu) interactions, and (ii) the fully frustrated nature of the antiferromagnet on the triangular lattice.

Magnetic Properties of Random-Mixture Graphite Intercalation Compounds

Abstract Random-mixture GICs such as stage-2 NicMn1-cCl2 GICs and stage-2 CocMn1-cCl2 GICs provide model systems for studying 2D random spin systems with spin frustration effects. The magnetic properties of these compounds have been studied by dc and ac magnetic susceptibility, and low field SQUID magnetization measurements. An irreversible effect of magnetization for stage-2 NicMni1-cCl2 GICs (0.8 ≤ c ≤ 1) and stage-2 CocNi1-cCl2 GICs (0 ≤ c ≤ 1) indicates an occurrence of cluster glass phase below a critical temperature where the spin directions of ferromagnetic clusters are frozen because of frustrated interisland interactions.

Replica Boundary Condition Applied to Random Spin Systems

We introduce a new boundary condition conjugate to any ordered phases including the spin glass. Using this boundary condition, we calculate an interfacial free energy in random spin systems, which is always non-negative irrespective of the bond configuration. It is possible to calculate a quantity relevant to the spin glass phase as a statistical average of random bond configurations. We apply this method to the asymmetric ± J Ising model in 2D and 3D. The results are consistent with the previous ones. We observe the scale invariance of the interfacial free energy by the present method at the critical point in 2D ( T =0), which is consistent with the power-law decaying spin glass correlation function.

Phase diagram of gauge glasses

The authors introduce a general class of random spin systems which are symmetric under local gauge transformations. Their model is a generalization of the usual Ising spin glass and includes the Zq, XY, and SU (2) gauge glasses. For this general class of systems, the internal energy and an upper bound on the specific heat are calculated explicitly in any dimensions on a special line in the phase diagram. Although the line intersects a phase boundary at a multicritical point, the internal energy and the bound on the specific heat are found to be written in terms of a simple function. They also show that the boundary between the ferromagnetic and nonferromagnetic phases is parallel to the temperature axis in the low-temperature region of the phase diagram. This means the absence of re-entrant transitions. All these properties are derived by simple applications of gauge transformations of spin and randomness degrees of freedom.

Kagomé antiferromagnet with defects: Satisfaction, frustration, and spin folding in a random spin system.

It is shown that site disorder induces noncoplanar states, competing with the thermal selection of coplanar states, in the nearest neighbor, classical kagome Heisenberg antiferromagnet (AFM). For weak disorder, it is found that the ground state energy is the sum of energies of separately satisfied triangles of spins. This implies that disorder does not induce conventional spin glass behavior. A transformation is presented, mapping ground state spin configurations onto a folded triangular sheet (a new kind of ``spin origami'') which has conformations similar to those of tethered membranes.

Inclusion of short-range order in a mean field theory for the disordered magnetic lattice gas

The disordered magnetic lattice gas (DMLG) as a unifying description of many simpler random spin systems has been investigated in an attempt to devise a mean field theory which goes beyond the infinitely-long-ranged model by incorporating short-range order (SRO). The authors have shown rigorously that the local thermodynamic properties of the DMLG on a Cayley tree of finite coordination number z are identical to the thermodynamic properties of the DMLG in a pair approximation obtained by using the method of the distribution function. Further, a modified pair approximation for the DMLG is presented which is exactly solvable. It is formulated for general random bond distribution functions, and is then examined for the special case of Gaussian distributions.

Replica optimization method for ground-state search of random spin systems

A new method to find ground states is proposed for random spin systems. The efficiency of this method is confirmed numerically in the case of the two-dimensional Ising spin glass with the gaussian bond-distribution in a uniform field. Increase of computational time with respect to system size is moderate and well fitted by a power-law up to L = 32. Magnetizations are calculated for various magnetic fields using the new method. Size dependence of the susceptibility is found to be χ(L) ∝ L x with x = 0.476(5). This value of the exponent x is somewhat larger than the predicted value by the droplet argument.

Magnetic properties of stage-2 NicMn1-cCl2-graphite intercalation compounds.

Stage-2 ${\mathrm{Ni}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$${\mathrm{Cl}}_{2}$-graphite intercalation compounds (with 0\ensuremath{\le}c\ensuremath{\le}1) are two-dimensional random-spin systems with competing ferromagnetic and antiferromagnetic exchange interactions. The magnetic properties of these compounds have been studied by dc and ac magnetic susceptibilities. The Curie-Weiss temperature increases monotonically with increasing Ni concentration, suggesting that both Ni and Mn ions are randomly distributed on the triangular-lattice sites of the ${\mathrm{Ni}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$${\mathrm{Cl}}_{2}$-intercalate layers. Its sign changes from negative to positive around c\ensuremath{\approxeq}0.22. The exchange interaction between Ni-Mn spin pairs is ferromagnetic and is described by J(Ni-Mn)=1.09[\ensuremath{\Vert}J(Ni-Ni)J(Mn-Mn)\ensuremath{\Vert}${]}^{1/2}$=1.44 K. The critical temperature ${\mathit{T}}_{\mathit{c}}$ decreases rapidly with a dilution of Mn. In spite of ferromagnetic J(Ni-Mn), the ferromagnetic long-range order of ${\mathrm{Ni}}^{2+}$ disappears below c\ensuremath{\approxeq}0.6. The large initial slope of [dln${\mathit{T}}_{\mathit{c}}$/dc${]}_{\mathit{c}=1}$=2.38 is ascribed to the two-dimensional Heisenberg-like character of stage-2 ${\mathrm{NiCl}}_{2}$-graphite intercalation compound. The critical behavior of these compounds shows a two-dimensional XY character. The critical exponent \ensuremath{\gamma} appears to be independent of c for c\ensuremath{\ge}0.7. It is determined that \ensuremath{\gamma}=2.27\ifmmode\pm\else\textpm\fi{}0.02 at c=0.9.

Numerical studies on random spin systems in a magnetic field

Several numerical results are reported about the low-temperature phase of the ± J Ising spin glass in three dimensions. The response of the central spin to random fields applied on the boundary spins is investigated. It is found that a weak homogeneous field suppresses this response. The overlaps of pairs of systems with different boundary fields are also calculated. The typical magnitude of the overlaps tends to zero, which indicates that q EA = 0 even in the case of a vanishing uniform field.

Structural and magnetic properties of stage-2 CocMn1-cCl2-graphite intercalation compounds.

Stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$${\mathrm{Cl}}_{2}$-graphite intercalation compounds (0\ensuremath{\le}c\ensuremath{\le}1) are two-dimensional random-spin systems with competing ferromagnetic and antiferromagnetic exchange interactions. The structural and magnetic properties of these compounds for 0\ensuremath{\le}c\ensuremath{\le}1 have been studied by x-ray diffraction and dc magnetic susceptibility. An analysis of the (00L) x-ray diffraction using a simple model developed here shows that these compounds are dominantly stage 2 but have a Hendricks-Teller-type staging disorder along the c axis. The c-axis repeat distance is proportional to the Co concentration, suggesting that both Co and Mn ions are randomly distributed on the triangular lattice of the ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$${\mathrm{Cl}}_{2}$ intercalate layers. The phase diagram determined from the dc magnetic susceptibility exhibits a ferromagnetic phase for 0.45\ensuremath{\le}c\ensuremath{\le}1.0. The Curie-Weiss temperature increases monotonically with increasing Co concentration. Its sign changes from negative to positive around c\ensuremath{\simeq}0.2. The exchange interaction between Co and Mn spins is ferromagnetic and is described by J(Co-Mn)=1.2 [\ensuremath{\Vert}J(Co-Co) J(Mn-Mn)\ensuremath{\Vert}${]}^{1/2}$=1.49 K. The average effective magnetic moment shows a minimum around c\ensuremath{\simeq}0.3, suggesting a partial replacement of ${\mathrm{Mn}}^{2+}$ ions by ${\mathrm{Mn}}^{+}$ or ${\mathrm{Mn}}^{3+}$ ions because of a charge transfer.

FMR linewidth in BaIn 1.5Fe 10.5O 19 single crystal

Ferromagnetic resonance, FMR, has been observed in a BaIn 1.5Fe 10.5O 19 ferrite single crystal. The FMR resonance field H res , effective linewidth ΔH eff , and effective Landau-Lifshitz-Gilbert damping parameter λ eff were obtained at 22.67 GHz for temperatures from 80 to 425 K and for two sample orientations in the applied field, namely perpendicular and parallel to the easy magnetization axis. The FMR parameters reveal anomalous values near the characteristic temperature T cr = 204 K in qualitative agreement with previous measurements of magnetization and magnetocrystalline anisotropy constants. The absorption line for all temperatures is Lorentzian and for T cr extreme exchange narrowing is observed with the correlation time of the dipolar field τ c ≈ 1.5×10 −13 s and the exchange constant J/k B ≈ 5 K . The effective linewidth for T < T cr fits the empirical formula ΔH eff = ΔH cr(T/T cr) -γcr . Since the present material at low temperatures can be classified as a random spin system, ΔH(T) has also been analysed in terms of another empirical form suggested previously: ΔΓ = Γ(T) − Γ 0 = Γ 1 exp(-T/T 0) . Agreement was obtained with this model for temperatures up to T 0 = 91 K . The effective parameter λ eff for T cr < T < T c is temperature independent and for T < T cr , dependent.

Ordering characterized by a strange attractor.

Competing trends of ordering are shown to allow for a novel low-temperature phase in random-spin systems. In the space of the moments of the distribution of exchange couplings, the renormalization-group flows are characterized by a strange attractor. A random-exchange Potts model on hierarchical lattices is studied to illustrate this phenomenon.

Dynamic critical behavior of random spin chains in a field.

The dynamic critical behavior of one-dimensional random spin systems in a field at zero temperature is investigated by a generalized transfer-matrix scaling technique. Three spin models are considered: Heisenberg in a longitudinal field, XY in a transverse field, and Ising in a transverse field, with either spin-glass or random-field disorder. Near the transition, i.e., for small values of the reduced field \ensuremath{\Delta}=(H-${H}_{c}$), where ${H}_{c}$ is the critical field, one finds that the dispersion relation for the low-frequency \ensuremath{\omega}, small-wave-vector k spin-wave excitations takes the scaling form \ensuremath{\omega}=${k}^{z}$f(\ensuremath{\Delta}/${k}^{\mathrm{cphi}}$), and exact results are given for the dynamic exponent z and crossover exponent cphi. This form contains a crossover of the frequency \ensuremath{\omega} between two different asymptotic behaviors: ${k}^{z}$ for \ensuremath{\Delta}\ensuremath{\ll}${k}^{\mathrm{cphi}}$ and ${h}^{\ensuremath{\delta}}$ for \ensuremath{\Delta}\ensuremath{\gg}${k}^{\mathrm{cphi}}$, where the field exponent is \ensuremath{\delta}=z/cphi. In the case of the Heisenberg systems the spin-glass disorder gives rise to the nontrivial dynamic exponent z=(3/2, whereas in the random-field case it is the exponent associated to the field that becomes nontrivial, taking the value (4/3. For the transverse XY systems the random-field disorder implies nontrivial values for both the dynamic and field exponents, (3/2 and (3/4, respectively, whereas the spin-glass disorder does not affect the dynamics of the system, which behaves like a pure transverse XY ferromagnet. Finally, for the transverse Ising systems neither the random field nor the spin-glass disorder affects the dynamics, which is the same as for a pure transverse Ising ferromagnet.