In a medium bowl mash avocados together with the lime juice. Stir in cilantro and garlic. Season with salt and cayenne pepper. Cover and refrigerate until needed.
Form ground chuck into 8 small patties. Heat a large skillet to medium-high heat. Add patties and cook, turning once until the hamburgers are fully cooked (the internal temperature has reached 160 degrees). Cut the 4 slices of pepper jack cheese into 4 squares. During the last few minutes of cooking top each patty with 2 of the cheese squares.
Cut slider buns in half and spread butter on the cut side of each bun. Place cut side down into a skillet over medium heat and cook until golden brown on the bottom.
To assemble sliders- place each hamburger patty onto the bottom half of a slider bun. Spread guacamole onto the bottom of the top half of the slider bun and place it over the patty.