What question did this study set out to answer?

Determine the functional form of the Landau free energy for structural phase transitions in a model solid and investigate the origin of anomalous critical exponents.

November 6, 1989Journal of Physics Condensed MatterOpen Access

What do Landau free energies really look like for structural phase transitions?

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Authors

AGA. P. GiddyUniversity of Cambridge MDMartin T. DoveQueen Mary University of London VHVolker HeineBridge University

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Implication

Molecular dynamics simulations reveal non-polynomial Landau free-energy behavior in model solids, highlighting the origin of non-standard critical exponents and widespread tricritical-like...

Key Points

Determine the functional form of the Landau free energy for structural phase transitions in a model solid and investigate the origin of anomalous critical exponents.
Calculated the Landau free-energy function analytically and via molecular dynamics simulations for a model solid with a local anharmonic double-well potential and mean-field inter-site coupling.
Evaluated polynomial expansions in terms of the order parameter across various model parameter ranges outside the Ginzburg fluctuation interval.
The calculated Landau free energy is not accurately represented by a standard low-order polynomial in the order parameter, independent of critical fluctuations in the Ginzburg interval.
Fitting a polynomial expansion demonstrates that the fourth-order coefficient varies strongly with temperature and remains small relative to the second-order coefficient across specific parameter regimes.
The temperature dependence and suppression of the fourth-order coefficient explain non-standard order parameter critical exponents and the frequent occurrence of tricritical-type behavior with beta approximately equal to 1/4.

Cite This Study

Giddy et al. (1989) studied this question.

synapsesocial.com/papers/6a9476f481fc78f0107085cb https://doi.org/10.1088/0953-8984/1/44/005

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November 6, 1989Journal of Physics Condensed MatterOpen Access

What do Landau free energies really look like for structural phase transitions?

View Full Paper

Ask AI

Bookmark

Authors

AGA. P. GiddyUniversity of Cambridge MDMartin T. DoveQueen Mary University of London VHVolker HeineBridge University

Discussion

Member takes

Implication

Molecular dynamics simulations reveal non-polynomial Landau free-energy behavior in model solids, highlighting the origin of non-standard critical exponents and widespread tricritical-like...

Key Points

Determine the functional form of the Landau free energy for structural phase transitions in a model solid and investigate the origin of anomalous critical exponents.
Calculated the Landau free-energy function analytically and via molecular dynamics simulations for a model solid with a local anharmonic double-well potential and mean-field inter-site coupling.
Evaluated polynomial expansions in terms of the order parameter across various model parameter ranges outside the Ginzburg fluctuation interval.
The calculated Landau free energy is not accurately represented by a standard low-order polynomial in the order parameter, independent of critical fluctuations in the Ginzburg interval.
Fitting a polynomial expansion demonstrates that the fourth-order coefficient varies strongly with temperature and remains small relative to the second-order coefficient across specific parameter regimes.
The temperature dependence and suppression of the fourth-order coefficient explain non-standard order parameter critical exponents and the frequent occurrence of tricritical-type behavior with beta approximately equal to 1/4.

Cite This Study

Giddy et al. (1989) studied this question.

synapsesocial.com/papers/6a9476f481fc78f0107085cb https://doi.org/10.1088/0953-8984/1/44/005

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