We calculate the Gibbs potential $\ensuremath{\Gamma}(M)$ of a one-dimensional metal at constant magnetization $M$ to second order in the screened electron-electron interaction $U$ . At zero temperature we find that $\ensuremath{\Gamma}(M)$ contains nonanalytic corrections proportional to ${M}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\ensuremath{\mid}M\ensuremath{\mid}$ and ${\ensuremath{\mid}M\ensuremath{\mid}}^{3}$, implying that a possible paramagnetic-ferromagnetic quantum phase transition in one-dimensional metals must be first order.We calculate the Gibbs potential $\ensuremath{\Gamma}(M)$ of a one-dimensional metal at constant magnetization $M$ to second order in the screened electron-electron interaction $U$. At zero temperature we find that $\ensuremath{\Gamma}(M)$ contains nonanalytic corrections proportional to ${M}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\ensuremath{\mid}M\ensuremath{\mid}$ and ${\ensuremath{\mid}M\ensuremath{\mid}}^{3}$, implying that a possible paramagnetic-ferromagnetic quantum phase transition in one-dimensional metals must be first order.

arXiv:cond-mat/0507608Physical Review BNov 3, 20052 citations

First-Order Phase Transitions

Wolfhard Janke E

Springer eBooksJan 1, 200333 citations

First- and second-order phase transitions in a system with multispin interactions

Amos Maritan, Attilio L. Stella, Carlo Vanderzande

A quantum model with $n$ -spin interactions is studied in the ground state. When $n\ensuremath{\rightarrow}\ensuremath{\infty}$ the model is solved exactly by mean-field theory and undergoes a first-order transition. The transition is expected to become second order for $n<{n}_{c}$ . With exploitation of self-duality and suitably improved mean-field approximations, a recently proposed criterion leads to the conjecture ${n}_{c}=3$ in one dimension. For the two-dimensional case the transition appears to be definitely of first order for $n=3 (2<{n}_{c}<3)$ .A quantum model with $n$-spin interactions is studied in the ground state. When $n\ensuremath{\rightarrow}\ensuremath{\infty}$ the model is solved exactly by mean-field theory and undergoes a first-order transition. The transition is expected to become second order for $n<{n}_{c}$. With exploitation of self-duality and suitably improved mean-field approximations, a recently proposed criterion leads to the conjecture ${n}_{c}=3$ in one dimension. For the two-dimensional case the transition appears to be definitely of first order for $n=3 (2<{n}_{c}<3)$.

Physical review. B, Condensed matterJan 1, 198420 citations

Nonuniversal critical behavior and first-order transitions in a coupled XY -Ising model

Jooyoung Lee, Enzo Granato, J. Michael Kosterlitz

We study, by a Migdal-Kadanoff approximation and Monte Carlo simulations, the phase diagram of a two-dimensional coupled XY-Ising model. This model can describe phase transitions in different systems with underlying continuous and ${\mathit{Z}}_{2}$ symmetries. Depending on the parameters, we find separate XY, Ising and first-order transitions. Also, a line of continuous transitions is found with simultaneous loss of XY and Ising order and varying critical exponents. The fully frustrated XY and Josephson-junction systems can be considered to lie along different paths in the model which can result in nonuniversal behavior if the transition is a single one.We study, by a Migdal-Kadanoff approximation and Monte Carlo simulations, the phase diagram of a two-dimensional coupled XY-Ising model. This model can describe phase transitions in different systems with underlying continuous and ${\mathit{Z}}_{2}$ symmetries. Depending on the parameters, we find separate XY, Ising and first-order transitions. Also, a line of continuous transitions is found with simultaneous loss of XY and Ising order and varying critical exponents. The fully frustrated XY and Josephson-junction systems can be considered to lie along different paths in the model which can result in nonuniversal behavior if the transition is a single one.

Physical review. B, Condensed matterSep 1, 199171 citations

We calculate the Gibbs potential $\ensuremath{\Gamma}(M)$ of a one-dimensional metal at constant magnetization

M

to second order in the screened electron-electron interaction

U

. At zero temperature we find that $\ensuremath{\Gamma}(M)$ contains nonanalytic corrections proportional to ${M}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\ensuremath{\mid}M\ensuremath{\mid}$ and ${\ensuremath{\mid}M\ensuremath{\mid}}^{3}$, implying that a possible paramagnetic-ferromagnetic quantum phase transition in one-dimensional metals must be first order.

A quantum model with

n

-spin interactions is studied in the ground state. When $n\ensuremath{\rightarrow}\ensuremath{\infty}$ the model is solved exactly by mean-field theory and undergoes a first-order transition. The transition is expected to become second order for

n<{n}_{c}

. With exploitation of self-duality and suitably improved mean-field approximations, a recently proposed criterion leads to the conjecture

{n}_{c}=3

in one dimension. For the two-dimensional case the transition appears to be definitely of first order for

n=3 (2<{n}_{c}<3)

{\mathit{Z}}_{2}

symmetries. Depending on the parameters, we find separate XY, Ising and first-order transitions. Also, a line of continuous transitions is found with simultaneous loss of XY and Ising order and varying critical exponents. The fully frustrated XY and Josephson-junction systems can be considered to lie along different paths in the model which can result in nonuniversal behavior if the transition is a single one.