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Magnetism: partition function

Having determined the magnetic energy levels eafiB) (as eigenvalues of the interaction Hamiltonian) we can proceed with the apparatus of the statistical thermodynamic by defining the (magnetic) partition function... [Pg.10]

X.2.2. The magnetic partition function expanded in seif-avoiding ioops... [Pg.275]

The partition function, H, Eq. (3), can be solved only approximately, e.g., in the MFA. However, from the magnetic analog one can obtain scaling relations for the concentration of links and polymer chains p, cf. Eq. (4)... [Pg.530]

There are in principle also energy levels associated with nuclear spins. In the absence of an external magnetic field, these are degenerate and consequently contribute a constant term to the partition function. As nuclear spins do not change during chemical reactions, we will ignore this contribution. [Pg.299]

The first illustration of the concept of a partition function is that of a two-level system, e.g. an electron in a magnetic field, with its spin either up or down (parallel or anti parallel to the magnetic field) (Fig. 3.2). The ground state has energy Eq = 0 and the excited state has energy Ae. By substituting these values in Eq. (3) we find the following partition function for this two-level system ... [Pg.82]

Magnetic functions are evaluated with the help of the partition function Z(T,B) and its derivatives. In order to perform the derivatives numerically, three values in the vicinity of the reference magnetic field are set, say Ei = Rref, B2 = Bref + 8, and IS3 = Eref + 28, where 8 is a small increment (8 = Bref/100). The calculations are then done for these fields, individually in each required direction of the magnetic field (a = x, y, z). With the energy levels i,Bk>a determined (k = 1 - 3), the partition function is summed up for individual fields... [Pg.39]

For an assembly of particles whose magnetic moments are much larger than the Bohr magneton, the partition function can be calculated as an integral over all possible values of 3. In this approximation, the averaging factor becomes in cubic symmetry (n = 4) ... [Pg.31]

When the number of spins is very large (i.e. in a magnetic material) the statistical thermodynamical formulae involving the partition function Z are the following ... [Pg.90]

From Eq. (4.53) we obtain the corresponding partition function of the Ising magnet by replacing H by its counterpart H given in Eq. (4.57), where,... [Pg.118]

That magnetism is a purely quantum mechanical phenomenon was discovered already in the 30s by Bohr and van Leeuwen, who showed that a classical partition function based on the Hamiltonian of electrons in a magnetic field does not depend on the magnetic field, and therefore ... [Pg.76]

The sum in Eq. III.20 is exactly the same as the partition function for the two-dimensional Ising model of antiferromagnetism in zero magnetic field, which function has been obtained by Onsager22 (see also Newell and Montroll 1). In terms of the parameter... [Pg.303]

Using Eq. 1, the partition function and thermal variation of the magnetic susceptibility of limited metallic units may be derived, allowing one to deduce, after comparison with experiment, the exchange parameters. A large number of polynuclear systems have been thoroughly investigated in this way. Clearly,... [Pg.57]

Hamiltonian, H energy levels et state vectors partition function, Z state functions, H, S, G, F magnetisation, M magnetic susceptibility x... [Pg.9]

Thermodynamic functions of magnetism in terms of the canonical partition function... [Pg.126]

A linkage between quantum theory (Hamiltonian, energy levels) and the macroscopic thermodynamical quantities (magnetisation, magnetic heat capacity, magnetic susceptibility) is given by statistical thermodynamics, in which the partition function adopts a key role. [Pg.129]


See other pages where Magnetism: partition function is mentioned: [Pg.437]    [Pg.406]    [Pg.71]    [Pg.194]    [Pg.269]    [Pg.199]    [Pg.56]    [Pg.51]    [Pg.336]    [Pg.118]    [Pg.63]    [Pg.427]    [Pg.448]    [Pg.177]    [Pg.49]    [Pg.280]    [Pg.224]    [Pg.169]    [Pg.157]    [Pg.221]    [Pg.67]    [Pg.118]    [Pg.56]    [Pg.135]    [Pg.76]    [Pg.437]    [Pg.124]    [Pg.813]    [Pg.835]    [Pg.881]   
See also in sourсe #XX -- [ Pg.289 , Pg.301 ]




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