Timeline for What are conditions for the existence of a critical value (for a phase transition)?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2012 at 10:14 | comment | added | genneth | In massless versions of QCD there is still a confinement energy scale even without any dimensionful coupling constants, due to [dimensional transmutation]( en.m.wikipedia.org/wiki/Dimensional_transmutation). | |
| Jan 23, 2012 at 8:12 | comment | added | Nikolaj-K | "It must contain some interaction constant with dimensions of energy" Why? | |
| Jan 22, 2012 at 21:42 | comment | added | yohBS | The Hamiltonian has dimensions of energy. It must contain some interaction constant with dimensions of energy (in the Ising model - the interaction $J$. In liquid-gas transition - the Lenard-Jones energy scale, etc..) | |
| Jan 22, 2012 at 21:34 | comment | added | propaganda | remember that in this picture the scaling of the axis is not constrained: in reality the Pressure axis is much much longer... | |
| Jan 22, 2012 at 19:12 | comment | added | Nikolaj-K | "And if you have a Hamiltonian, you have an energy scale" Why, necessarily? | |
| Jan 22, 2012 at 18:21 | comment | added | yohBS | I cannot imagine such a case. If the phase transition occurs as a function of $T$, this means that you're working with a Hamiltonian, and average expressions of the form $e^{-\beta H}$. And if you have a Hamiltonian, you have an energy scale. | |
| Jan 22, 2012 at 16:10 | comment | added | Nikolaj-K | I mean that if there is no smallest natural unit (not just some random energy unit for counting, but a physical scale), then I don't see why such a thing as a critical temperature could even emerge. I ask therefore if a critical temperature can only exist in a model with some natural unit (atom radius was my example) which makes up the formula for $T_c$. | |
| Jan 22, 2012 at 15:29 | comment | added | yohBS | If you set $k_b=1$, and there's no reason not to do so, then temperature is measured energy units. So clearly, if you multiply ALL energy scales in your system by 2, then $T_c$ will also be multiplied by 2. This is what I meant. I can't quite understand your question beyond that. | |
| Jan 22, 2012 at 13:42 | comment | added | Nikolaj-K | thx for the response. In "it is clear, on physical grounds, that the critical temperature will scale as some basic energy scale of the system", what does "the critical temperature will scale" mean? My main question if the value where phase transitions occur due to some other distinguished scale (such as atom radius). | |
| Jan 22, 2012 at 12:52 | history | answered | yohBS | CC BY-SA 3.0 |