The squat and deadlift are two of the best exercises you can perform. In addition to primarily strengthening the hamstrings, quads and glutes, both rely on the muscles in your core to stabilize the weight and your entire body during the lift. These muscles include the rectus and transverse abdominis, external and internal obliques, and the spinal erectors. The hypertrophy -- or growth of these muscles -- will not be large enough to increase the width of your waist.
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Core Muscle Locations
Your abdominals are in the front of your waist and contain an outer and inner layer -- the rectus abdominis and transverse abdominis. Similarly, the obliques contain an external and internal layer as well. The deeper layers contain small and thin muscles that have almost no potential for hypertrophy. The spinal erectors are the muscles of the core along your vertebrae. The thickest and most muscular portion of your erectors is in your lower spine, near the waist.
Core Muscle Functions
When contracted, the abdominals pull your trunk forward, the erectors pull your trunk backward and the obliques pull your trunk to their respective sides. When all of these muscles contract, they negate each others' effects, causing a neutral spine -- the position of your back that is regarded as good posture. The transverse abdominis and internal obliques help to facilitate this process by providing extra compression of your trunk. The largest portion of the spinal erectors, in the lower back, is actually the most likely to increase in size.
Squats and Deadlifts
When squatting, your abdominals prevent your spine from overarching, the obliques help to keep your body and the bar from tilting to the left or right and the erectors work to facilitate an upright posture and keep your torso from collapsing under the weight. The lower portion of the erectors is activated more during the squat than deadlift.
By contrast, the upper lumbar erectors, which are just above the waist and closer to your ribcage, are worked during the deadlift. Your abdominals and obliques keep your spine from arching and your body from shifting to one side or the other allowing you to keep the weight level. Your spinal erectors contract hard to prevent the weight below from pulling your back down into a dangerous and rounded position, which can cause a slipped disc over time.
Nutrition will ultimately be a much more important factor to the size of your waistline than exercise. To increase your muscle mass, you need to consume more calories than you burn, but if you take in far more calories -- particularly from unhealthy foods -- than you burn, you may gain body fat. Monitor your food intake. Eat plenty of vegetables, lean sources of protein and whole-wheat products. If you eat fewer calories than you burn through exercise, you will see little or no increase to the size of your waist during these exercises because you will not gain fat or muscle mass.