We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations.There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.

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This publication includes all data on superconductive materials intercepted through March 1975. Dala on the bulk elements have been critically evaluated. and values on alloys. compounrl~. anti nth"T forms have been selected and condensed to indicate the probable value and spread of values observed. Prov"n non-superconductors have been noted. Conflict in data values has been noted. All data have been ,keyed to the literature in one or more of the tables. Special subdivisions are presented for $uperconduc· t~ve materials with organic constituents and for those based on semiconductive materials. The proper-tIes. ~res~nted are superconductive critical temperature, critical magnetic fields, material state and com· posItIOn mclu~ing crystal-structure type where noted, a key to thin-film forms, and the presence of thermodynamlc data (generally the electronic specific heat, 'Y, and Debye 6). High-magnetic·field superconductors are noted with listing 01' He,. H c ' He" and He, plus the temperature of observation T.~5

In a random solid solution, if the two atoms have appreciably different sizes, the nearest-neighbor distances and to a lesser extent the higher neighbor distances will be of three kinds, γAA, γAB, and γBB. The effect produces modulations in the diffuse intensity similar to those produced by short-range order. The size effect is important when the difference in scattering power is large, the difference in size is large, and the short-range order is small. The size effect is illustrated by a single crystal pattern of Cu3Au and a powder pattern of Ni3Au2. An asymmetry in the wings about a fundamental reflection is a result of the size effect.

The intermetallic compound, BiMn, has been studied by neutron diffraction at temperatures from 4.2°K to 733°K (460°C). In the temperature range 340-360°C to 445°C a disordered arrangement of Mn atoms on regular and interstitial lattice sites fits the data well if the Mn atoms are assumed to be in the paramagnetic state. This model conflicts with the suggestion made by Guillaud of an antiferromagnetic state in this temperature range. The temperature hysteresis associated with both magnetization and the large cell distortions are qualitatively explained by the disordering and recovery at the transformation temperatures. The effective moment per Mn atom below the transformation agrees with the magnetic measurements of Heikes within experimental error. Measurements of spin direction made at temperatures below 84°K show that only partial rotation occurs in zero magnetic field.

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As computers increase in speed and memory, scientists are inevitably led to simulate more complex systems over larger time and length scales. Although a simple, straightforward algorithm is often the most efficient for small system sizes, especially when the time needed to implement the algorithm is included, the scaling of time and memory with system size becomes crucial for larger simulations.In our studies of hysteresis and avalanches in a simple model of magnetism (the random-field Ising model at zero temperature), we often have found it necessary to do very large simulations. Previous simulations were limited to relatively small systems (up to 900 2 and 128 3 [1], see however [3]). In our simulations we have found that larger systems (up to a billion spins) are crucial to extracting accurate values of the universal critical exponents and understanding important qualitative features of the physics.We have developed two efficient and relatively straightforward algorithms which allow us to simulate these large systems. The first algorithm uses sorted lists and scales as O(N log N ), and asymptotically uses N × (sizeof(double)+sizeof(int)) bytes of memory, where N is the number of spins. The second algorithm, which does not generate the random fields, also scales in time as O(N log N ), but asymptotically needs only one bit of storage per spin, about 96 times less than the first algorithm. Using the latter algorithm, simulations of a billion spins can be run on a workstation with 128MB of RAM in a few hours.In this column we discuss algorithms for simulating the zero-temperature random-field Ising model, which is defined by the energy functionwhere the spins s i = ±1 sit on a D-dimensional hypercubic lattice with periodic boundary conditions. The spins interact ferromagnetically with their z nearest neighbors ; Olga Perković is with McKinsey & Company, olga perkovic@mckinsey.com; Karin Dahmen has just joined the physics faculty of the University of Illinois at Urbana-Champaign; Bruce W. Roberts is working at Starwave Corporation in Seattle, bwr@halcyon.com; James P. Sethna is a professor of physics at Cornell University, sethna@lassp.cornell.edu. Details about his research group can be found at http://www.lassp.cornell.edu/sethna/ with strength J, and experience a uniform external field H(t) and a random local field h i . We choose units such that J = 1. The random field h i is distributed according to the Gaussian distribution ρ(h) of width R:The external field H(t) is increased arbitrarily slowly from −∞ to ∞.The dynamics of our model includes no thermal fluctuations: each spin flips deterministically when it can gain energy by doing so. That is, it flips when its local fieldchanges sign. This change can occur in two ways: a spin can be triggered when one of its neighbors flips (by participating in an avalanche), or a spin can be triggered because of an increase in the external field H(t) (starting a new avalanche). The zero-temperature random-field Ising model was introduced by Robbins and Ji [3] to study flu...

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