TY - JOUR

T1 - Theory of ferromagnetism and the ordering of electronic energy levels

AU - Lieb, Elliott

AU - Mattis, Daniel

PY - 1962

Y1 - 1962

N2 - Consider a system of N electrons in one dimension subject to an arbitrary symmetric potential, V(x1, xN), and let E(S) be the lowest energy belonging to the total spin value S. We have proved the following theorem: E(S)<E(S′) if S<S′. Hence, the ground state is unmagnetized. The theorem also holds in two or three dimensions (although it is possible to have degeneracies) provided V(x1, y1, z1; xN, yN, zN) is separately symmetric in the xi, yi, and zi. The potential need not be separable, however. Our theorem has strong implications in the theory of ferromagnetism because it is generally assumed that for certain repulsive potentials, the ground state is magnetized. If such be the case, it is a very delicate matter, for a plausible theory must not be so general as to give ferromagnetism in one dimension, nor in three dimensions with a separately symmetric potential.

AB - Consider a system of N electrons in one dimension subject to an arbitrary symmetric potential, V(x1, xN), and let E(S) be the lowest energy belonging to the total spin value S. We have proved the following theorem: E(S)<E(S′) if S<S′. Hence, the ground state is unmagnetized. The theorem also holds in two or three dimensions (although it is possible to have degeneracies) provided V(x1, y1, z1; xN, yN, zN) is separately symmetric in the xi, yi, and zi. The potential need not be separable, however. Our theorem has strong implications in the theory of ferromagnetism because it is generally assumed that for certain repulsive potentials, the ground state is magnetized. If such be the case, it is a very delicate matter, for a plausible theory must not be so general as to give ferromagnetism in one dimension, nor in three dimensions with a separately symmetric potential.

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U2 - 10.1103/PhysRev.125.164

DO - 10.1103/PhysRev.125.164

M3 - Article

AN - SCOPUS:36149025693

SN - 0031-899X

VL - 125

SP - 164

EP - 172

JO - Physical Review

JF - Physical Review

IS - 1

ER -