A survey of pre/post-test data using the Halloun–Hestenes Mechanics Diagnostic test or more recent Force Concept Inventory is reported for 62 introductory physics courses enrolling a total number of students N=6542. A consistent analysis over diverse student populations in high schools, colleges, and universities is obtained if a rough measure of the average effectiveness of a course in promoting conceptual understanding is taken to be the average normalized gain 〈g〉. The latter is defined as the ratio of the actual average gain (%〈post〉−%〈pre〉) to the maximum possible average gain (100−%〈pre〉). Fourteen “traditional” (T) courses (N=2084) which made little or no use of interactive-engagement (IE) methods achieved an average gain 〈g〉T-ave=0.23±0.04 (std dev). In sharp contrast, 48 courses (N=4458) which made substantial use of IE methods achieved an average gain 〈g〉IE-ave=0.48±0.14 (std dev), almost two standard deviations of 〈g〉IE-ave above that of the traditional courses. Results for 30 (N=3259) of the a...

/pdf/interactive-engagement-versus-traditional-methods-a-six-308kycdryk.pdf

Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses

The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their interrelations. The experimental observations are surveyed and the analogies between different physical systems - fluids, magnets, superfluids, binary alloys, etc. - are developed phenomenologically. An exact theoretical basis for the analogies follows from the equivalence between classical and quantal `lattice gases' and the Ising and Heisenberg-Ising magnetic models. General rigorous inequalities for critical exponents at and below Tc are derived. The nature and validity of the `classical' (phenomenological and mean field) theories are discussed, their predictions being contrasted with the exact results for plane Ising models, which are summarized concisely. Pade approximant and ratio techniques applied to appropriate series expansions lead to precise critical-point estimates for the three-dimensional Heisenberg and Ising models (tables of data are presented). With this background a critique is presented of recent theoretical ideas: namely, the `droplet' picture of the critical point and the `homogeneity' and `scaling' hypotheses. These lead to a `law of corresponding states' near a critical point and to relations between the various exponents which suggest that perhaps only two or three exponents might be algebraically independent for any system.

https://iopscience.iop.org/article/10.1088/0034-4885/30/2/306/pdf

The theory of equilibrium critical phenomena

“…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...

Experiments on simple magnetic model systems

A survey is given of the physical properties, composition and crystal structure of intermetallic compounds formed between rare-earth elements and 3d transition elements. Apart from binary compounds the results of pseudobinary series are also considered. The magnetic properties determined by the exchange interactions involving 4f as well as 3d electrons, are discussed together with experimental results available on magnetovolume effects and various resonance techniques such as NMR and the Mossbauer effect.

https://iopscience.iop.org/article/10.1088/0034-4885/40/10/002/pdf

Intermetallic compounds of rare-earth and 3d transition metals

This paper compares theory and experiment for behavior very near critical points. The primary experimental results are the "critical indices" which describe singularities in various thermodynamic derivatives and correlation functions. These indices are tabulated and compared with theory. The basic theoretical ideas are introduced via the molecular field approach, which brings in the concept of an order parameter and suggests that there are close relations among different phase transition problems. Although this theory is qualitatively correct it is quantitatively wrong, it predicts the wrong values of the critical indices. Another theoretical approach, the "scaling law" concept, which predicts relations among these indices, is described. The experimental evidence for and against the scaling laws is assessed. It is suggested that the scaling laws provide a promising approach to understanding phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.

Static Phenomena Near Critical Points: Theory and Experiment

The raising of angular momentum degeneracy of f-Electron terms by cubic crystal fields

The spin-lattice relaxation time of Ce3+ in cerium magnesium nitrate has been measured as a function of temperature and of magnetic fields up to 1000 gauss. In the temperature range between 3° and 1.9°K, the relaxation time is found to vary exponentially with inverse temperature, changing by a factor of 350. A theoretical treatment of spin-lattice relaxation appropriate to rare earth salts leads to predictions which agree both with the experimentally observed temperature dependence and with the magnitude of the relaxation time. The dominant relaxation process is one in which a phonon of high energy (» kT) is absorbed by the spin system resulting in a transition from one of the ground state doublet levels to the nearest excited level. Then, in a separate step, another high energy phonon is emitted and a transition is effected to the other level of the ground state doublet. The net result of this `two-step direct process' can be interpreted as spin-lattice relaxation; i.e. there results a net change in population between the ground state doublet levels which brings the spin system towards thermal equilibrium with the lattice. Such a mechanism, which is quite different from those which have been envisaged up to now for spin-lattice relaxation, should be appropriate for many of the rare earth salts.

http://iopscience.iop.org/article/10.1088/0370-1328/77/2/305/pdf

Spin-Lattice Relaxation in Cerium Magnesium Nitrate at Liquid Helium Temperature: A New Process

The factors that make certain magnetic materials behave similarly to corresponding Ising models are reviewed. Examples of extensively studied materials include Dy(C2H5SO4)3.9H2) (DyES), Dy3Al5O12 (DyAlG), DyPO4, Dy2Ti2O7, LiTbF4, K2CoF4, and Rb2CoF4. Various comparisons between theory and experiment for these materials are examined. The agreement is found to be generally very good, even when there are clear differences between the ideal Ising model and the real materials. In a number of experiments behavior has been observed that requires extensions of the usual Ising model. These include the effects of long range magnetic dipole interactions, competing interaction effects in field-induced phase transitions, induced staggered field effects and frustration effects, and dynamic effects. The results show that the Ising model and real magnetic materials have provided an unusually rich and productive field for the interaction between theory and experiment over the past 40 years.

/pdf/the-ising-model-and-real-magnetic-materials-3ujp0hh1hk.pdf

The Ising model and real magnetic materials

A tunnel diode oscillator is described which has been successfully used for paramagnetic susceptibility measurements at frequencies from 3 to 55 MHz, at temperatures from 1.2 to 77 K, and at magnetic fields up to 18 kG. In appropriate cases, such measurements may be used to infer magnetic specific heats and spin‐lattice relaxation times.

Magnetic Susceptibility Measurements with a Tunnel Diode Oscillator

The specific heat of the linear-chain magnet ${\mathrm{CsNiF}}_{3}$ has been measured at temperatures between 4 and 18 K, in magnetic fields up to 8 kG (0.8 T). A rounded peak is observed in both the temperature and field dependence. The peak positions in the field dependence are in qualitative agreement with classical soliton theory and they are also consistent with neutron-scattering estimates of the soliton rest energy. Quantitative comparisons indicate the need for extensions of the theory.

W. P. Wolf

Papers

The raising of angular momentum degeneracy of f-Electron terms by cubic crystal fields

Spin-Lattice Relaxation in Cerium Magnesium Nitrate at Liquid Helium Temperature: A New Process

The Ising model and real magnetic materials

Magnetic Susceptibility Measurements with a Tunnel Diode Oscillator

Specific Heat of CsNiF 3 : Evidence for Spin Solitons