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In the last two decades low-dimensional (low-d) physics has matured into a major branch of science. Quite generally we may define a system with restricted dimensionality d as an object that is infinite only in one or two spatial directions (d = 1 and 2). Such a definition comprises isolated single chains or layers, but also fibres and thin layers (films) of varying but finite thickness. Clearly, a multitude of physical phenomena, notably in solid state physics, fall into these categories. As examples, we may mention: ? Magnetic chains or layers (thin-film technology). ? Metallic films (homogeneous or heterogeneous, crystalline, amorphous or microcristalline, etc.). ? I-d or 2-d conductors and superconductors. ? Intercalated systems. ? 2-d electron gases (electrons on helium, semiconductor interfaces). ? Surface layer problems (2-d melting of monolayers of noble gases on a substrate, surface problems in general). ? Superfluid films of ~He or 'He. ? Polymer physics. ? Organic and inorganic chain conductors, superionic conductors. ? I-d or 2-d molecular crystals and liquid crystals. ? I-d or 2-d ferro- and antiferro electrics.

In the last two decades low-dimensional (low-d) physics has matured into a major branch of science. Quite generally we may define a system with restricted dimensionality d as an object that is infinite only in one or two spatial directions (d = 1 and 2). Such a definition comprises isolated single chains or layers, but also fibres and thin layers (films) of varying but finite thickness. Clearly, a multitude of physical phenomena, notably in solid state physics, fall into these categories. As examples, we may mention: ? Magnetic chains or layers (thin-film technology). ? Metallic films (homogeneous or heterogeneous, crystalline, amorphous or microcristalline, etc.). ? I-d or 2-d conductors and superconductors. ? Intercalated systems. ? 2-d electron gases (electrons on helium, semiconductor interfaces). ? Surface layer problems (2-d melting of monolayers of noble gases on a substrate, surface problems in general). ? Superfluid films of ~He or 'He. ? Polymer physics. ? Organic and inorganic chain conductors, superionic conductors. ? I-d or 2-d molecular crystals and liquid crystals. ? I-d or 2-d ferro- and antiferro electrics.

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to Low-Dimensional Magnetic Systems.- 1. Experimental realizations of 2-d magnetic systems.- 2. Magnetic model Hamiltonians.- 3. Survey of the predicted magnetic behaviour.- 4. Lattice- and spin-dimensionality crossovers in quasi 2-d magnetic systems.- 5. Magnetic and nonmagnetic impurity doping in quasi 2-d magnets.- References.- Theory of Two-Dimensional Magnets.- 1. Introduction.- 2. Ising magnets.- 2.1. Ising model. Excitations and phase transitions.- 2.2. Onsager solution.- 2.3. Critical exponents and scaling.- 2.4. Dual transformation. Order and disorder.- 3. Planar magnets.- 3.1. XY model.- 3.2. Excitations.- 3.3. Scaling and correlations.- 3.4. Phase transition.- 3.5. Magnetic vortices as a Coulomb gas.- 3.6. Relationships with other models.- 3.7. Planar antiferromagnets.- 4. Heisenberg magnets.- 4.1. Heisenberg model and real magnets.- 4.2. Renormailzation of the temperature.- 4.3. Heisenberg ferromagnets in an external magnetic field.- 4.4. Excitations of the 2-d Heisenberg model.- 4.5. Dipolar interactions.- 5. Experimental layered magnets.- 5.1. Ising layered magnets. ANNNI model: application to CeSb and CeBi.- 5.2. Layered planar magnets.- 5.3. Layered Heisenberg magnets.- 6. Dynamics of 2-d magnets.- 6.1. Equations of motion.- 6.2. Spin-wave dynamics.- 6.3. Spin-diffusion dynamics.- 6.4. Dynamics of localized excitations.- 6.5. Resonant paramagnetic cxcitation of vortex pairs.- 6.6. Summary.- Acknowledgement.- References.- Application of High- and Low-Temperature Series Expansions to Two-Dimensional Magnetic Systems.- 1. Introduction.- 1.1. Series expansions.- 1.2. Methods applied in series analysis.- 1.2.1. Ratio methods.- 1.2.2. Pade approximant methods.- 1.2.3. Other methods of series analysis.- 2. Series expansions and predictions for the 2-d Ising model.- 2.1. Spin 1/2 model with nearest neighbours only (simple 2-d lattices).- 2.1.1. High-temperature series.- 2.1.2. Low-temperature series.- 2.1.3. Properties in nonzero parallel field.- 2.1.4. Properties in nonzero perpendicular field.- 2.2. Ising model with general S.- 2.3. Other series for I (1/2).- 2.3.1. Restricted dimensionality systems.- 2.3.2. Further-neighbour interactions.- 2.3.3. Crossover from 2-d to 3-d behaviour.- 3. Series expansions and predictions for the Heisenberg model.- 3.1. Series for S = 1/2, arbitrary S and S = ?.- 3.1.1. Properties at nonzero field.- 3.2. Other series for the Heisenberg model.- 3.2.1. Restricted dimensionality.- 3.2.2. Further-neighbour interactions.- 3.2.3. Crossover from 2-d to 3-d behaviour.- 4. Series expansion in the X Y and Ising-Heisenberg models.- 4.1. Series for the 2-d XY model.- 4.2. Series for the 2-d Ising-Heisenberg model.- 5. Applications to magnetic systems.- 5.1. Ising model.- 5.2. Heisenberg model.- 5.2.1. Spin 1/2.- 5.2.2. Spin 1.- 5.2.3. Spin 3/2 and spin 2.- 5.2.4. Spin 5/2.- 5.2.5. Restricted dimensionality.- 5.3. XY and Ising-Heisenberg models.- Acknowledgements.- References.- Spin Waves in Two-Dimensional Magnetic Systems: Theory and Applications.- 1. Introduction.- 2. Magnetic structures and spin Hamiltonians.- 3. Spin wave theory of model systems.- 4. Dispersion relation.- 5. Thermodynamic properties.- 6. Impurities in antiferromagnets.- References.- Neutron Scattering Experiments on Two-Dimensional Heisenberg and Ising Magnets.- 1. Introduction.- 2. 2-d systems with Ising and Heisenberg interactions.- 2.1. K2CoF4: a 2-d Ising system.- 2.2. K2FeF4: a 2-d planar antiferromagnet.- 2.3. K2MnF4 and K2NiF4: weakly anisotropic Heisenberg magnets.- 2.4. Rb2CrCl4: a planar Heisenberg ferromagnet with small anisotropy.- 2.5. K2CuF4: a planar Heisenberg ferromagnet.- 3. 2-d random magnetic systems.- 3.1. Phase transitions and critical phenomena.- 3.2. Excitations.- 3.3. Random field effects.- 3.4. Relaxation front 2-d to 3-d order.- 3.5. Competing anisotropics and interactions.- 4. Triangular lattice antiferromagnet (TALAF).- 4.1. Fluctuations.- 4.2. An additional degree of freedom.- 4.3. Perturbati

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