Does wax go through a sharp phase transition when it melts? When ice melts, the system goes sharply from being solid to being liquid. There is no intermediate state where it is soft. This is a true phase transition. The thermodynamic potential is not an analytic function of its parameters.
Does the same happen for wax? In my experience in playing with candles, I have seen solid and liquid wax and I notices that, when the wax is heating up, it becomes easier to stick a match in it. I have however never done systematic experimentation and never gone through the trouble of looking for scientific literature on the problem. Does anyone know about this? Does wax change sharply from being solid to liquid as it heats up or is there a smooth cross-over?
PS: Even though my question can be answered by a simple yes/no, I would very much appreciate a detailed answer. Why is wax different/similar to water when it melts? If the answer is 'no', what happens at the transition? Is it a smoothed out version of the phase transition of water or is there a bigger difference?
PPS: I have the same question about chocolate. What can you tell me?
 A: Polymers such as wax definitely undergo phase transitions.  You inquired about paraffin wax, which is oil-based.
Paraffin wax is made of long rod-like molecules called linear straight-chain alkanes.  It's solid at room temperature, but when refined as liquid paraffin and combined with water, it can act as liquid crystal, which complicates its phase diagram.
Liquid crystal is a phase all to itself.  There are other phases within the liquid crystal phase.  In the nematic phase, the long rod-like paraffin molecules all point in the same direction but have no positional structure.  In the smectic phase, molecules tend to form layers (for example, slippery soap that collects in the bottom of a soap dish is smectic liquid crystal).  In the cholesteric phase, the layers corkscrew around an imaginary axis.  Here's a description of these and other liquid crystal phases: http://plc.cwru.edu/tutorial/enhanced/files/lc/phase/phase.htm.
The phase diagrams of polymers like paraffin may not look like the phase diagrams you're familiar with.  Depending on how the paraffin molecule is altered in refining, its phase attributes will change.  It may be liquid at room temperature, or solid.  The phase diagram may change if paraffin combines with water, because when treated with other materials it can be a surfactant/emulsifier.  One end of the molecule can be hydrophilic while the other is hydrophobic, and in that case the phase diagram will be altered.  Unlike a pure element, paraffin can have many phase diagrams depending on the refinery process that produced it, additives, and other substances with which it combines.
One reason you may have trouble noticing the phase transitions of wax is that heat doesn't flow immediately through a wax blob.  The outer layers soften and liquify first.  Here's a link to a study of phase transitions in paraffin: http://www.ijettjournal.org/volume-2/issue2/IJETT-V2I2P213.pdf.
Chocolate is not a polymer, but inexpensive chocolate may be mixed with paraffin to give it polymer-like qualities such as surface sheen and smoothness.  When you're dealing with composite substances such as chocolate, the phase diagram may not plot pressure against temperature.  For example, here is a link to a study of the six polymorphic phases of chocolate: http://link.springer.com/article/10.1007%2Fs11746-998-0245-y.  And here is an explanation of those phases: http://patentimages.storage.googleapis.com/WO2012135279A1/imgf000006_0001.png.  Here's a phase diagram that plots cooling time against temperature, which shows how chocolate needs the optimal combination of temperature and cooling time to form the most desirable phase structure (scroll down to the phase diagram): http://soft-matter.seas.harvard.edu/index.php/The_Science_of_Chocolate:_interactive_activities_on_phase_transitions,_emulsification,_and_nucleation.
A: This comes down to the fact that ice is a crystal, and wax (and chocolate) is a (glassy) polymer-like material.
Here is the chart of stiffness of a polymer as it is heated.  When it is cold, the polymer is in a glassy phase.  As it is heated, it enters the "leathery phase", and it begins to soften.  As it warms up more, the material becomes progressively softer, as the molecular bonds are weakened by the additional energy.

In contrast, a graph for ice (or another comparable crystalline material) would look like a vertical cliff.  On one side it is ice (solid), and on the other side it is liquid.
In fact, you could say that wax never actually freezes: it just becomes an increasingly viscous liquid.
EDIT: As I have been reminded in the comments, polymers are capable of being crystals, but are typically in a glassy configuration, and so all references to polymers above are for polymers in a glassy configuration.
A: Ice has a sharp melting point temperature because it is a pure substance.  Wax is a mixture of higher molecular weight hydrocarbons, so it doesn't have the same sharp melting point.  While I have petrochemical experience in my background, I didn't work much with waxes, so I can't give you a firm estimate of the composition, but I suspect that web searches can provide more specific examples.
