In this work we use field-theoretic and renormalization-group methods to study the finite-temperature ferromagnetic phase transition in the three-dimensional Hubbard model. We show that the nature of the ferromagnetic transition may strongly depend on the constraint imposed on the system. For example, if the system is allowed to exchange particles with a reservoir, the stability criterion for the occurrence of a continuous phase transition can be calculated using the mean-field approximation. On the other hand, if the total charge is conserved and charge- and spin-density fluctuations are considered in the theory, a different criterion, quite distinct from the mean-field one, is found, resulting in a fluctuation-induced renormalized Heisenberg tricritical point. The tricritical behavior is studied by calculating the one-loop renormalized free energy and using scaling analysis to determine the tricritical exponents. Finally, the exact solution of the model in the spherical limit and near the ferromagnetic transition is presented, in which case no fluctuation-induced tricritical point is found.In this work we use field-theoretic and renormalization-group methods to study the finite-temperature ferromagnetic phase transition in the three-dimensional Hubbard model. We show that the nature of the ferromagnetic transition may strongly depend on the constraint imposed on the system. For example, if the system is allowed to exchange particles with a reservoir, the stability criterion for the occurrence of a continuous phase transition can be calculated using the mean-field approximation. On the other hand, if the total charge is conserved and charge- and spin-density fluctuations are considered in the theory, a different criterion, quite distinct from the mean-field one, is found, resulting in a fluctuation-induced renormalized Heisenberg tricritical point. The tricritical behavior is studied by calculating the one-loop renormalized free energy and using scaling analysis to determine the tricritical exponents. Finally, the exact solution of the model in the spherical limit and near the ferromagnetic transition is presented, in which case no fluctuation-induced tricritical point is found.

Physical review. B, Condensed matterAug 1, 199315 citations

Crossover scaling functions for two-point correlations near tricritical points

W. K. Theumann

The expectations of phenomenological crossover scaling theory are worked out for two-point correlation functions in zero field above the primary critical point. Renormalization-group recursion relations are then used to construct the two-point correlation function for the changeover from tricritical to critical-line behavior, above the tricritical point, to first order in $\ensuremath{\epsilon}=4\ensuremath{-}d$, for $3\ensuremath{\le}d<4$. An explicit expression is obtained for the normalized double-scaling function ${\stackrel{^}{\ensuremath{\Gamma}}}_{N}({q}^{2}{\ensuremath{\xi}}^{2}, \frac{g}{{t}^{\ensuremath{\phi}}})$, for the general scaling variable ${q}^{2}{\ensuremath{\xi}}^{2}$, and the crossover variable $w=\frac{g}{{t}^{\ensuremath{\phi}}}$, $q\ensuremath{\ll}{a}^{\ensuremath{-}1}$ being the wave vector; $\ensuremath{\xi}\ensuremath{\gg}a$ is a second-moment correlation length and $a$ the lattice spacing. In the tricritical regime, $w\ensuremath{\simeq}0$, ${\stackrel{^}{\ensuremath{\Gamma}}}_{N}$ ( ${x}^{2}, w$ ) has the Ornstein-Zernicke form and the changeover to the critical regime $w\ensuremath{\simeq}\ensuremath{\infty}$ is explicitly discussed. The limitation of the results, within our calculations to first order in $\ensuremath{\epsilon}$, are pointed out.The expectations of phenomenological crossover scaling theory are worked out for two-point correlation functions in zero field above the primary critical point. Renormalization-group recursion relations are then used to construct the two-point correlation function for the changeover from tricritical to critical-line behavior, above the tricritical point, to first order in $\ensuremath{\epsilon}=4\ensuremath{-}d$, for $3\ensuremath{\le}d<4$. An explicit expression is obtained for the normalized double-scaling function ${\stackrel{^}{\ensuremath{\Gamma}}}_{N}({q}^{2}{\ensuremath{\xi}}^{2}, \frac{g}{{t}^{\ensuremath{\phi}}})$, for the general scaling variable ${q}^{2}{\ensuremath{\xi}}^{2}$, and the crossover variable $w=\frac{g}{{t}^{\ensuremath{\phi}}}$, $q\ensuremath{\ll}{a}^{\ensuremath{-}1}$ being the wave vector; $\ensuremath{\xi}\ensuremath{\gg}a$ is a second-moment correlation length and $a$ the lattice spacing. In the tricritical regime, $w\ensuremath{\simeq}0$, ${\stackrel{^}{\ensuremath{\Gamma}}}_{N}$ (${x}^{2}, w$) has the Ornstein-Zernicke form and the changeover to the critical regime $w\ensuremath{\simeq}\ensuremath{\infty}$ is explicitly discussed. The limitation of the results, within our calculations to first order in $\ensuremath{\epsilon}$, are pointed out.

Physical review. B, Condensed matterDec 1, 19784 citations

Dynamics of fluctuations at multicritical points

Vladimir V. Prudnikov, G. B. Teǐtel'Baum

Journal of Experimental and Theoretical PhysicsJan 1, 19770 citations

Behaviour of systems near the polycritical point

A.Z. Patashinsky, B.I. Shumilo

Physics Letters AApr 1, 19770 citations

Crossover Phenomena, Critical and Tricritical Phase Transitions

Eberhard K. Riedel

A theory for tricritical phenomena proposed by Wegner and the author is described on an elementary level. The emphasis of the discussion is on (i) the differences between critical and tricritical phase transitions, (ii) the crossover phenomena that occur near tricritical points, and (iii) the determination of tricritical exponents, scaling fields and scaling functions. The results have been obtained by renormalization‐group techniques and a scaling field approach to crossover phenomena. The elements of these techniques are briefly explained.A theory for tricritical phenomena proposed by Wegner and the author is described on an elementary level. The emphasis of the discussion is on (i) the differences between critical and tricritical phase transitions, (ii) the crossover phenomena that occur near tricritical points, and (iii) the determination of tricritical exponents, scaling fields and scaling functions. The results have been obtained by renormalization‐group techniques and a scaling field approach to crossover phenomena. The elements of these techniques are briefly explained.

Annual Conference on Magnetism and Magnetic Materials (MMM)Jan 1, 19741 citation

a

the lattice spacing. In the tricritical regime, $w\ensuremath{\simeq}0$, ${\stackrel{^}{\ensuremath{\Gamma}}}_{N}$ (

{x}^{2}, w

) has the Ornstein-Zernicke form and the changeover to the critical regime $w\ensuremath{\simeq}\ensuremath{\infty}$ is explicitly discussed. The limitation of the results, within our calculations to first order in $\ensuremath{\epsilon}$, are pointed out.